35th@MSC2020-2：离散数学/代数学@20251101
| 03-XX Mathematical logic and foundations 03-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations 03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations 03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 03-03 History of mathematical logic and foundations [Consider also classification numbers pertaining to Section 01] 03-04 Software, source code, etc. for problems pertaining to mathematical logic and foundations 03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations 03-08 Computational methods for problems pertaining to mathematical logic and foundations 03-11 Research data for problems pertaining to mathematical logic and foundations |
03-XX数理逻辑与基础 03-00数理逻辑与基础相关的一般参考文献（手册、词典、参考书目等） 03-01导论性阐述（教材、辅导论文、 等）涉及数理逻辑与基础理论 03-02数理逻辑与基础理论研究（含专著、综述性论文） 03-03数学逻辑与基础理论发展史[另请参阅第01节的分类编号] 03-04与问题相关的软件、源代码等 数学逻辑与基础 03-06会议记录、会议、文集等 数学逻辑与基础 03-08数学逻辑与基础问题的计算方法 03-11数学相关问题的研究数据 逻辑与基础 |
| 03Axx Philosophical aspects of logic and foundations 03A05 Philosophical and critical aspects of logic and foundations {For philosophy of mathematics, see also 00A30} 03A10 Logic in the philosophy of science 03A99 None of the above, but in this section |
03Axx逻辑学的哲学方面和基础 03A05逻辑与基础的哲学与批判性研究（数学哲学参见00A30） 03A10科学哲学中的逻辑 03A99以上都不是，但属于本节 |
| 03Bxx General logic 03B05 Classical propositional logic 03B10 Classical first-order logic 03B16 Higher-order logic 03B20 Subsystems of classical logic (including intuitionistic logic) 03B22 Abstract deductive systems 03B25 Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] 03B30 Foundations of classical theories (including reverse mathematics) [See also 03F35] 03B35 Mechanization of proofs and logical operations [See also 68V15] 03B38 Type theory 03B40 Combinatory logic and lambda calculus [See also 68N18] 03B42 Logics of knowledge and belief (including belief change) 03B44 Temporal logic 03B45 Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45} 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects, see 03F52} 03B48 Probability and inductive logic [See also 60A05] 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05] 03B53 Paraconsistent logics 03B55 Intermediate logics 03B60 Other nonclassical logic 03B62 Combined logics 03B65 Logic of natural languages [See also 68T50, 91F20] 03B70 Logic in computer science [See also 68-XX] 03B80 Other applications of logic 03B99 None of the above, but in this section |
03Bxx通用逻辑 03B05逻辑学 03B10一阶经典逻辑 03B16高阶逻辑 03B20经典逻辑的子系统（包含直觉主义 逻辑 03B22抽象演绎系统 03B25理论与句子集合的可判定性[另见11U05、12L05、20F10] 03B30古典理论基础（含逆向理论） 数学）[另见03F35] 03B35证明与逻辑运算的机械化[另见68V15] 03B38类型理论 03B40组合逻辑与λ演算[另见68N18] 03B42知识与信念的逻辑（含信念改变） 03B44时间逻辑 03B45模态逻辑（包括规范逻辑）{知识与信念参见03B42；时间逻辑参见03B44；可证明性逻辑另见03F45} 03B47亚结构逻辑（包括相关性、蕴含关系、 线性逻辑、Lambek演算、BCK和BCI逻辑）{证明理论相关部分请参见03F52} 03B48概率与归纳逻辑[另见60A05] 03B50多值逻辑 03B52模糊逻辑；模糊性逻辑[另见68T27、68T37、94D05] 03B53一致逻辑 03B55中级逻辑 03B60其他非经典逻辑 03B62组合逻辑 03B65自然语言逻辑[另见68T50,91F20] 03B70计算机科学中的逻辑[另见68-XX] 03B80其他逻辑应用 03B99以上都不是，但属于本节 |
| 03Cxx Model theory 03C05 Equational classes, universal algebra in model theory [See also 08Axx, 08Bxx, 18C05] 03C07 Basic properties of first-order languages and structures 03C10 Quantifier elimination, model completeness and related topics 03C13 Model theory of finite structures [See also 68Q15, 68Q19] 03C15 Model theory of denumerable and separable structures 03C20 Ultraproducts and related constructions 03C25 Model-theoretic forcing 03C30 Other model constructions 03C35 Categoricity and completeness of theories 03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts in model theory [See also 03C48] 03C48 Abstract elementary classes and related topics [See also 03C45] 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 03C55 Set-theoretic model theory 03C57 Computable structure theory, computable model theory [See also 03D45] 03C60 Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 03C62 Models of arithmetic and set theory [See also 03Hxx] 03C64 Model theory of ordered structures; o-minimality 03C65 Models of other mathematical theories 03C66 Continuous model theory, model theory of metric structures 03C68 Other classical first-order model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48] 03C85 Second- and higher-order model theory 03C90 Nonclassical models (Boolean-valued, sheaf, etc.) 03C95 Abstract model theory 03C98 Applications of model theory [See also 03C60] 03C99 None of the above, but in this section |
03Cxx模型理论 03C05等式类，模型论中的泛代数[另见08Axx、08Bxx、18C05] 03C07一阶语言与结构的基本性质 03C10量词消去、模型完备性及相关议题 03C13有限结构模型理论[另见68Q15、68Q19] 03C15可数与可分结构的模型理论 03C20超级产品及相关结构 03C25模型理论强制 03C30其他模型结构 03C35理论的确定性与完备性 03C40插值、保全、可定义性 03C45分类理论、稳定性及相关概念 在模型理论中[另见03C48] 03C48简单类和相关主题[另见03C45] 03C50具有特殊性质的型号（饱和、刚性等） 03C52模型类的属性 03C55集合论模型论 03C57可计算结构理论，可计算模型理论[另见03D45] 03C60模论代数[另见08C10、12Lxx、13L05] 03C62算术与集合论模型[另见03Hxx] 03C64有序结构的模型理论；o-极小性 03C65其他数学理论的模型 03C66连续模型论，度量结构的模型论 03C68其他经典一阶模型理论 03C70可接受集合的逻辑 03C75其他无限逻辑 03C80带额外量词和运算符的逻辑[另见03B42、03B44、03B45、03B48] 03C85二阶及高阶模型理论 03C90非经典模型（布尔值、层等） 03C95抽象模型论 03C98模型论的应用[另见03C60] 03C99以上都不是，但属于本节 |
| 03Dxx Computability and recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15] 03D10 Turing machines and related notions [See also 68Q04] 03D15 Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17] 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities in computability and recursion theory 03D32 Algorithmic randomness and dimension [See also 68Q30] 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. in computability and recursion theory [See also 06B25, 08A50, 20F10, 68R15] 03D45 Theory of numerations, effectively presented structures [See also 03C57] {For intuitionistic and similar approaches, see 03F55} 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies of computability and definability 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D78 Computation over the reals, computable analysis {For constructive aspects, see 03F60} 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section |
03Dxx可计算性与递归理论 03D03 Thue和Post系统等。 03D05自动机与形式文法的关联 附带逻辑性问题[另见68Q45、68Q70、 68R15] 03D10图灵机及相关概念[另见 68Q04] 03D15计算复杂度（含隐式计算） （计算复杂度）[另见68Q15、68Q17] 03D20递归函数与关系，子递归 等级制度 03D25递归（可计算）可枚举集合与 程度 03D28其他图灵学位结构 03D30计算能力中的其他度量与可约性 以及递归理论 03D32算法随机性与维度[另见 68Q30] 03D35无法判定性与句子集合的度量 03D40 Word问题等在可计算性和递归中的应用 理论[另见06B25、08A50、20F10、68R15] 03D45数字理论，有效呈现 结构（参见03C57）{适用于直觉主义和 类似方法，参见03F55} 03D50集合与结构的递归等价类型 岛屿 03D55可计算性与可定义性的层级结构 03D60序数的可计算性与递归理论 可接受的集合等。 03D65高阶与集合递归理论 03D70诱导可定义性 03D75摘要、公理化可计算性与递归 理论 03D78实数域上的计算，可计算分析（有关构造性内容，请参见03F60） 03D80可计算性与递归理论的应用 03D99 以上均不适用，但本节适用 |
| 03Exx Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also 28A05, 54H05] 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin’s axiom [See also 03E57] 03E55 Large cardinals 03E57 Generic absoluteness and forcing axioms [See also 03E50] 03E60 Determinacy principles 03E65 Other set-theoretic hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Theory of fuzzy sets, etc. 03E75 Applications of set theory 03E99 None of the above, but in this section |
03Exx集合论 03E02分区关系 03E04有序集及其余界；pcf理论 03E05其他组合集合论 03E10序数和基数 03E15描述性集合论[另见28A05、54H05] 03E17连续统的枢轴特征 03E20其他经典集合论（包括函数、关系和集合代数） 03E25选择公理及相关命题 03E30经典集合论及其片段的公理化 03E35 一致性和独立性结果 03E40强制执行的其他方面与布尔值模型 03E45内部模型，包含可构造性、序定义性及核心模型 03E47集合论可定义性的其他概念 03E50连续统假设和马丁公理[另见03E57] 03E55大红雀 03E57一般绝对性与强制公理[另见03E50] 03E60确定性原理 03E65其他集合论假设和公理 03E70非经典和二阶集合论 03E72模糊集理论等。 03E75集合论的应用 03E99以上都不是，但属于本节 |
| 03Fxx Proof theory and constructive mathematics 03F03 Proof theory, general (including proof-theoreticsemantics) 03F05 Cut-elimination and normal-form theorems 03F07 Structure of proofs 03F10 Functionals in proof theory 03F15 Recursive ordinals and ordinal notations 03F20 Complexity of proofs 03F25 Relative consistency and interpretations 03F30 First-order arithmetic and fragments 03F35 Second- and higher-order arithmetic and fragments [See also 03B30] 03F40 G¨odel numberings and issues of incompleteness 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25] 03F50 Metamathematics of constructive systems 03F52 Proof-theoretic aspects of linear logic and othersubstructural logics [See also 03B47] 03F55 Intuitionistic mathematics 03F60 Constructive and recursive analysis [See also03B30, 03D45, 03D78, 26E40, 46S30, 47S30] 03F65 Other constructive mathematics [See also 03D45]03F99 None of the above, but in this section |
03Fxx证明理论与构造性数学 03F03一般证明论（含证明论语义学） 03F05截消定理与标准型定理 03F07证明结构 03F10证明理论中的函数 03F15递归序数和序数记号 03F20证明的复杂性 03F25相对一致性与解释 03F30一阶算术和碎片 03F35二阶及高阶算术与片段 [另见03B30] 03F40 Godel编号与不完全性问题 03F45可证明性逻辑及相关代数（例如对角化 代数）[另见03B45、03G25、06E25]03F50构造系统元数学 03F52线性逻辑及其他子结构逻辑的证明理论方面[另见03B47] 03F55直觉数学 03F60构造性与递归分析[另见03B30、03D45、03D78、26E40、46S30、47S30] 03F65其他构造数学[另见03D45] 03F99以上均非，但本节 |
| 03Gxx Algebraic logic 03G05 Logical aspects of Boolean algebras [See also 06Exx] 03G10 Logical aspects of lattices and related structures [See also 06Bxx] 03G12 Quantum logic [See also 06C15, 81P10] 03G15 Cylindric and polyadic algebras; relation algebras 03G20 Logical aspects of Lukasiewicz and Post algebras [See also 06D25, 06D30] 03G25 Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 03G27 Abstract algebraic logic 03G30 Categorical logic, topoi [See also 18B25, 18C05, 18C10] 03G99 None of the above, but in this section |
03Gxx代数逻辑 03G05布尔代数的逻辑特性[另见 06Exx] 03G10格子及相关结构的逻辑方面 [另见06Bxx] 03G12量子逻辑[另见06C15、81P10] 03G15圆柱与多面体代数；关系代数 03G20 Lukasiewicz和Post代数的逻辑方面 [另见06D25、06D30] 03G25与逻辑相关的其他代数[另见03F45， 06D20, 06E25, 06F35] 03G27抽象代数逻辑 03G30分类逻辑，主题[另见18B25、18C05、18C10] 03G99以上都不是，但属于本节 |
| 03Hxx Nonstandard models [See also 03C62] 03H05 Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 03H10 Other applications of nonstandard models (economics, physics, etc.) 03H15 Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05] 03H99 None of the above, but in this section |
03Hxx非标准型号[另请参阅 03C62] 03H05数学中的非标准模型[另见26E35、28E05、30G06、46S20、47S20、54J05] 03H10非标准模型的其他应用（经济学， 物理等） 03H15算术的非标准模型[另见11U10、12L15、13L05] 03H99以上都不是，但属于本节 |
| 05-XX Combinatorics {For finite fields, see 11Txx} 05-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics 05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics 05-03 History of combinatorics [Consider also classification numbers pertaining to Section 01] 05-04 Software, source code, etc. for problems pertaining to combinatorics 05-06 Proceedings, conferences, collections, etc. pertaining to combinatorics 05-08 Computational methods for problems pertaining to combinatorics 05-11 Research data for problems pertaining to combinatorics |
05-XX组合数学（适用于有限 字段，参见11Txx} 05-00组合数学相关参考文献（手册、词典、书目等） 05-01导论性阐述（教材、辅导论文、（等）与组合数学相关的 05-02组合数学领域的研究论文（含专著、综述文章） 05-03组合数学史[另见分类] 与第01节相关的数字] 05-04与问题相关的软件、源代码等 组合数学 05-06会议记录、会议、文集等 组合数学 05-08组合数学问题的计算方法 05-11组合数学问 |
| 05Axx Enumerative combinatorics {For enumeration in graph theory, see 05C30} 05A05 Permutations, words, matrices 05A10 Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 05A15 Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05A16 Asymptotic enumeration 05A17 Combinatorial aspects of partitions of integers [See also 11P81, 11P82, 11P83] 05A18 Partitions of sets 05A19 Combinatorial identities, bijective combinatorics 05A20 Combinatorial inequalities 05A30 q-calculus and related topics [See also 33Dxx] 05A40 Umbral calculus 05A99 None of the above, but in this section |
05Axx枚举组合学{For 图论中的枚举法，参见05C30} 05A05排列、单词、矩阵 05A10阶乘、二项式系数、组合函数[另见11B65、33Cxx] 05A15精确枚举问题，生成函数 [另见33Cxx、33Dxx] 05A16渐近计数 05A17整数划分的组合方面[另见11P81、11P82、11P83] 05A18集合划分 05A19组合恒等式，双射组合学 05A20组合不等式 05A30 q-微积分及相关主题[另见33Dxx] 05A40临界点计算 05A99以上都不是，但属于本节 |
| 05Bxx Designs and configurations {For applications of design theory, see 94C30} 05B05 Combinatorial aspects of block designs [See also 51E05, 62K10] 05B07 Triple systems 05B10 Combinatorial aspects of difference sets (numbertheoretic, group-theoretic, etc.) [See also 11B13] 05B15 Orthogonal arrays, Latin squares, Room squares 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 05B25 Combinatorial aspects of finite geometries [See also 51D20, 51Exx] 05B30 Other designs, configurations [See also 51E30] 05B35 Combinatorial aspects of matroids and geometric lattices [See also 52B40, 90C27] 05B40 Combinatorial aspects of packing and covering [See also 11H31, 52C15, 52C17] 05B45 Combinatorial aspects of tessellation and tiling problems [See also 52C20, 52C22] 05B50 Polyominoes 05B99 None of the above, but in this section |
05Bxx设计与配置{适用于应用程序 设计理论，参见94C30} 05B05区组设计的组合学方面[另见51E05、62K10] 05B07三联系统 05B10差集的组合特性（数论， （群论等）[另见11B13] 05B15正交阵列、拉丁方阵、房间方阵 05B20矩阵的组合特性（关联矩阵、哈达玛矩阵等） 05B25有限几何的组合方面[另见51D20,51Exx] 05B30其他设计、配置[另见51E30] 05B35拟阵与几何格的组合论方面[另见52B40、90C27] 05B40包装与覆盖的组合方面[另见11H31、52C15、52C17] 05B45镶嵌与铺砌问题的组合数学方面[另见52C20、52C22] 05B50多米诺骨牌 05B99以上都不是，但属于本节 |
| 05Cxx Graph theory {For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15} 05C05 Trees 05C07 Vertex degrees [See also 05E30] 05C09 Graphical indices (Wiener index, Zagreb index, Randi´c index, etc.) 05C10 Planar graphs; geometric and topological aspects of graph theory [See also 57K10, 57M15] 05C12 Distance in graphs 05C15 Coloring of graphs and hypergraphs 05C17 Perfect graphs 05C20 Directed graphs (digraphs), tournaments 05C21 Flows in graphs 05C22 Signed and weighted graphs 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 05C30 Enumeration in graph theory 05C31 Graph polynomials 05C35 Extremal problems in graph theory [See also 90C35] 05C38 Paths and cycles [See also 90B10] 05C40 Connectivity 05C42 Density (toughness, etc.) 05C45 Eulerian and Hamiltonian graphs 05C48 Expander graphs 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C51 Graph designs and isomorphic decomposition [See also 05B30] 05C55 Generalized Ramsey theory [See also 05D10] 05C57 Games on graphs (graph-theoretic aspects) [See also 91A43, 91A46] 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C62 Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10} 05C63 Infinite graphs 05C65 Hypergraphs 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C72 Fractional graph theory, fuzzy graph theory 05C75 Structural characterization of families of graphs 05C76 Graph operations (line graphs, products, etc.) 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C80 Random graphs (graph-theoretic aspects) [See also 60B20] 05C81 Random walks on graphs 05C82 Small world graphs, complex networks (graphtheoretic aspects) [See also 90Bxx, 91D30] 05C83 Graph minors 05C85 Graph algorithms (graph-theoretic aspects) [See also 68R10, 68W05] 05C90 Applications of graph theory [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 05C92 Chemical graph theory [See also 92E10] 05C99 None of the above, but in this section |
05Cxx图论{应用领域 图表，参见68R10、81Q30、81T15、82B20， 82C20, 90C35, 92E10, 94C15} 05C05树木 05C07顶点度数[另见05E30] 05C09图论指标（维纳指数、萨格勒布指数、兰迪奇指数等） 05C10平面图；图论的几何与拓扑方面[另见57K10、57M15] 05C12图中的距离 05C15图与超图着色 05C17完美图 05C20有向图（digraphs），锦标赛 05C21图中的流 05C22签名和加权图 05C25图论与抽象代数（群、环、域等）[另见20F65] 05C30图论中的枚举 05C31图多项式 05C35图论中的极值问题[另见90C35] 05C38路径和循环[另请参见90B10] 05C40连接 05C42密度（韧性等） 05C45欧拉图与哈密顿图 05C48扩展图 05C50图论与线性代数（矩阵、特征值等） 05C51图设计与同构分解[另见05B30] 05C55广义Ramsey理论[另见05D10] 05C57图上的游戏（图论方面）[另见91A43、91A46] 05C60图论中的同构问题（重构） 猜想等）与同态（子图嵌入等） 05C62图形表示法（几何与交集） （如表示法等）{关于图表绘制，请参见68R10} 05C63无限图 05C65超图 05C69具有特殊属性的顶点子集（主导性） 集合、独立集、团等） 05C70边子集具有特殊性质（因式分解， 匹配、划分、覆盖和打包等） 05C72分数图论，模糊图论 05C75图族的结构特征分析 05C76图运算（线图、乘积等） 05C78图标记（优雅图、带宽等） 05C80随机图（图论方面）[另见60B20] 05C81图上的随机游走 05C82小世界图与复杂网络（图论） （方面）[另见90Bxx、91D30] 05C83图子式 05C85图算法（图论方面）[另见68R10、68W05] 05C90图论的应用[另见68R10、81Q30、81T15、82B20、82C20、90C35、92E10、94C15] 05C92化学图论[另见92E10] 05C99以上都不是，但属于本节 |
| 05Dxx Extremal combinatorics 05D05 Extremal set theory 05D10 Ramsey theory [See also 05C55] 05D15 Transversal (matching) theory 05D40 Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) 05D99 None of the above, but in this section |
05Dxx极限组合学 05D05极限集合论 05D10 Ramsey理论[另见05C55] 05D15横向（匹配）理论 05D40极端组合学中的概率方法，包括多项式方法（组合零点定理， 等 05D99以上都不是，但属于本节 |
| 05Exx Algebraic combinatorics 05E05 Symmetric functions and generalizations 05E10 Combinatorial aspects of representation theory [See also 20C30] 05E14 Combinatorial aspects of algebraic geometry [See also 14Nxx] 05E16 Combinatorial aspects of groups and algebras [See also 22E45, 33C80] 05E18 Group actions on combinatorial structures 05E30 Association schemes, strongly regular graphs 05E40 Combinatorial aspects of commutative algebra 05E45 Combinatorial aspects of simplicial complexes 05E99 None of the above, but in this section |
05Exx代数组合学 05E05对称函数和推广 05E10表示理论的组合方面[另见20C30] 05E14代数几何的组合方面[另见14Nxx] 05E16群与代数的组合方面[另见22E45、33C80] 05E18组合结构上的群作用 05E30关联图，强正则图 05E40交换代数的组合方面 05E45单纯复形的组合方面 05E99以上都不是，但属于本节 |
| 06-XX Order, lattices, ordered algebraic structures [See also 18B35] 06-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures 06-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures 06-02 Research exposition (monographs, survey articles) pertaining to ordered structures 06-03 History of ordered structures [Consider also classification numbers pertaining to Section 01] 06-04 Software, source code, etc. for problems pertaining to ordered structures 06-06 Proceedings, conferences, collections, etc. pertaining to ordered structures 06-08 Computational methods for problems pertaining to ordered structures 06-11 Research data for problems pertaining to ordered structures |
06-XX序，格，有序代数 结构[另见18B35] 06-00与有序结构相关的通用参考文献（手册、词典、参考书目等） 06-01 导论性阐述（教科书、论文、（等）与有序结构相关的 06-02关于有序结构的研究论文（包括专著、综述文章） 06-03有序结构的历史[另请参阅分类] 与第01节相关的数字] 06-04与问题相关的软件、源代码等 有序结构 06-06与会议、会议记录、文集等相关的 有序结构 06-08计算机方法在有序结构相关问题中的应用 06-11有序结构相关问题的研究数据 |
| 06Axx Ordered sets 06A05 Total orders 06A06 Partial orders, general 06A07 Combinatorics of partially ordered sets 06A11 Algebraic aspects of posets 06A12 Semilattices [See also 20M10] {For topological semilattices, see 22A26} 06A15 Galois correspondences, closure operators (in relation to ordered sets) 06A75 Generalizations of ordered sets 06A99 None of the above, but in this section |
06Axx订购的套件 06A05总订单 06A06部分序，一般 06A07部分有序集的组合学 06A11偏序集的代数方面 06A12半格[另见20M10]{关于拓扑半格，参见22A26} 06A15伽罗瓦对应与闭包算子（有序集相关） 06A75有序集的推广 06A99以上都不是，但属于本节 |
| 06Bxx Lattices [See also 03G10] 06B05 Structure theory of lattices 06B10 Lattice ideals, congruence relations 06B15 Representation theory of lattices 06B20 Varieties of lattices 06B23 Complete lattices, completions 06B25 Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10] 06B30 Topological lattices [See also 06F30, 22A26, 54F05, 54H12] 06B35 Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55] 06B75 Generalizations of lattices 06B99 None of the above, but in this section |
06Bxx网格[另请参见03G10] 06B05晶格结构理论 06B10格理想，同余关系 06B15格的表示理论 06B20格子的种类 06B23完整格子，补全 06B25自由格、射影格、文字问题[另见03D40、08A50、20F10] 06B30拓扑晶格[另见06F30、22A26、54F05、54H12] 06B35连续格和偏序集，应用[另见06B30、06D10、06F30、18B35、22A26、68Q55] 06B75格的推广 06B99以上都不是，但属于本节 |
| 06Cxx Modular lattices, complemented lattices 06C05 Modular lattices, Desarguesian lattices 06C10 Semimodular lattices, geometric lattices 06C15 Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10] 06C20 Complemented modular lattices, continuous geometries 06C99 None of the above, but in this section 06Dxx Distributive lattices 06D05 Structure and representation theory of distributive lattices 06D10 Complete distributivity 06D15 Pseudocomplemented lattices 06D20 Heyting algebras (lattice-theoretic aspects) [See also 03G25] 06D22 Frames, locales {For topological questions, see 54-XX} 06D25 Post algebras (lattice-theoretic aspects) [See also 03G20] 06D30 De Morgan algebras, Lukasiewicz algebras (lattice-theoretic aspects) [See also 03G20] 06D35 MV-algebras 06D50 Lattices and duality 06D72 Fuzzy lattices (soft algebras) and related topics 06D75 Other generalizations of distributive lattices 06D99 None of the above, but in this section |
06Cxx模格，补强 格子框架 06C05模格，Desarguesian格 06C10半模块化格，几何格 06C15补充格与正补格 和偏序集[另见03G12、81P10] 06C20补充模块化格栅，连续几何结构 06C99 以上均不适用，但本节适用 06Dxx分布式格子 06D05分配结构与表征理论 格子框架 06D10完全分配律 06D15补格子 06D20黑廷代数（格论方面）[参见 也即03G25] 06D22框架，局部{拓扑问题请参见54-XX} 06D25后代数（格论方面）[另见03G20] 06D30 De Morgan代数，Lukasiewicz代数（格论方面）[另见03G20] 06D35 MV代数 06D50格子与对偶性 06D72模糊格（软代数）及相关课题 06D75分布格的其他推广形式 06D99以上都不是，但属于本节 |
| 06Exx Boolean algebras (Boolean rings) [See also 03G05] 06E05 Structure theory of Boolean algebras 06E10 Chain conditions, complete algebras 06E15 Stone spaces (Boolean spaces) and related structures 06E20 Ring-theoretic properties of Boolean algebras [See also 16E50, 16G30] 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45] 06E30 Boolean functions [See also 94D10] 06E75 Generalizations of Boolean algebras 06E99 None of the above, but in this section |
06Exx布尔代数（布尔环） [另见03G05] 06E05布尔代数结构理论 06E10链条件，完备代数 06E15石质空间（布尔空间）及相关结构 06E20 布尔代数的环论性质[另见16E50,16G30] 06E25带附加运算的布尔代数（可对角化） 代数等）[另见03G25、03F45] 06E30布尔函数[另见94D10] 06E75布尔代数的推广 06E99以上都不是，但属于本节 |
| 06Fxx Ordered structures 06F05 Ordered semigroups and monoids [See also20Mxx] 06F07 Quantales 06F10 Noether lattices 06F15 Ordered groups [See also 20F60] 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40] 06F25 Ordered rings, algebras, modules {For ordered fields, see 12J15} [See also 13J25, 16W80] 06F30 Ordered topological structures (aspects of ordered structures) [See also 06B30, 22A26, 54F05, 54H12] 06F35 BCK-algebras, BCI-algebras (aspects of ordered structures) [See also 03G25] 06F99 None of the above, but in this section |
06Fxx有序结构 06F05有序半群与幺半群[另见20Mxx] 06F07 量子格 06F10诺特格子 06F15有序基团[另见20F60] 06F20有序阿贝尔群、Riesz群、有序线性空间[另见46A40] 06F25有序环、代数、模（关于有序域，参见12J15）[另见13J25、16W80] 06F30有序拓扑结构（有序结构的特征） 结构)[另见06B30、22A26、54F05、54H12] 06F35 BCK-代数、BCI-代数（有序结构的方面）[另见03G25] 06F99以上都不是，但属于本节 |
| 08-XX General algebraic systems 08-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems 08-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems 08-02 Research exposition (monographs, survey articles) pertaining to general algebraic systems 08-03 History of general algebraic systems [Consider also classification numbers pertaining to Section 01] 08-04 Software, source code, etc. for problems pertaining to general algebraic systems 08-06 Proceedings, conferences, collections, etc. pertaining to general algebraic systems 08-08 Computational methods for problems pertaining to general algebraic systems 08-11 Research data for problems pertaining to general algebraic systems |
08-XX一般代数系统 08-00通用参考书（手册、词典等） 与一般代数相关的参考文献等 系统 08-01导论性阐述（教材、辅导论文、 （等）与一般代数系统相关的 08-02研究论文（专著、综述性文章） 关于一般代数系统 08-03一般代数系统的历史[另见 与第01节相关的分类编号] 08-04与问题相关的软件、源代码等 到一般代数系统 08-06与会议、会议记录、文集等相关的 到一般代数系统 08-08与问题相关的计算方法 到一般代数系统 08-11与一般问题有关的研究数据 代数系统 |
| 08Axx Algebraic structures [See also 03C05] 08A02 Relational systems, laws of composition 08A05 Structure theory of algebraic structures 08A30 Subalgebras, congruence relations 08A35 Automorphisms and endomorphisms of algebraic structures 08A40 Operations and polynomials in algebraic structures, primal algebras 08A45 Equational compactness 08A50 Word problems (aspects of algebraic structures) [See also 03D40, 06B25, 20F10, 68R15] 08A55 Partial algebras 08A60 Unary algebras 08A62 Finitary algebras 08A65 Infinitary algebras 08A68 Heterogeneous algebras 08A70 Applications of universal algebra in computer science 08A72 Fuzzy algebraic structures 08A99 None of the above, but in this section |
08Axx代数结构[另见 03C05] 08A02关系系统，组合定律 08A05代数结构的结构理论 08A30子代数，同余关系 08A35代数的自同构与自同态 结构 08A40代数结构中的运算与多项式 原始代数 08A45等式紧致性 08A50 Word问题（代数结构的方面） [另见03D40、06B25、20F10、68R15] 08A55部分代数 08A60一元代数 08A62有限代数 08A65无穷代数 08A68异构代数 08A70泛代数在计算机科学中的应用 08A72 模糊代数结构 08A99以上都不是，但属于本节 |
| 08Bxx Varieties [See also 03C05] 08B05 Equational logic, Mal’tsev conditions 08B10 Congruence modularity, congruence distributivity 08B15 Lattices of varieties 08B20 Free algebras 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also 18A30] 08B26 Subdirect products and subdirect irreducibility 08B30 Injectives, projectives 08B99 None of the above, but in this section |
08Bxx品种[另见03C05] 08B05等式逻辑，马尔采夫条件 08B10同余模结构与同余分配律 08B15 簇格 08B20免费代数 08B25产品、混合产品及其他类型的极限与余极限[另见18A30] 08B26子直积与子直积不可约性 08B30注射器，投射器 08B99以上都不是，但属于本节 |
| 08Cxx Other classes of algebras 08C05 Categories of algebras [See also 18C05] 08C10 Axiomatic model classes [See also 03Cxx, in particular 03C60] 08C15 Quasivarieties 08C20 Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30] 08C99 None of the above, but in this section |
08Cxx其他代数类 08C05代数的分类[另见18C05] 08C10公理模型类[另见03Cxx，特别是 03C60] 08C15 Quasivarieties 08C20代数类的自然对偶性[另见06E15、18A40、22A30] 08C99以上都不是，但属于本节 |
| 11-XX Number theory 11-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11-03 History of number theory [Consider also classification numbers pertaining to Section 01] 11-04 Software, source code, etc. for problems pertaining to number theory 11-06 Proceedings, conferences, collections, etc. pertaining to number theory 11-11 Research data for problems pertaining to number theory |
11-XX数论 11-00与数论相关的通用参考文献（手册、词典、参考书目等） 11-01导论性阐述（教材、辅导论文、 等）与数论相关的 11-02数论研究论文（含专著、综述文章） 11-03数论史[另见分类] 与第01节相关的数字] 11-04软件、源代码等与问题相关的内容 到数论 11-06与会议、会议记录、收藏品等相关的 到数论 11-11与数论相关问题的研究数据 |
| 11Axx Elementary number theory {For analogues in number fields, see 11R04} 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors 11A07 Congruences; primitive roots; residue systems 11A15 Power residues, reciprocity 11A25 Arithmetic functions; related numbers; inversion formulas 11A41 Primes 11A51 Factorization; primality 11A55 Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 11A63 Radix representation; digital problems {For metric results, see 11K16} 11A67 Other number representations 11A99 None of the above, but in this section |
11Axx小学数论课程（适用于 数域中的类似情形，参见11R04} |
| 11Bxx Sequences and sets 11B05 Density, gaps, topology 11B13 Additive bases, including sumsets [See also 05B10] 11B25 Arithmetic progressions [See also 11N13] 11B30 Arithmetic combinatorics; higher degree uniformity 11B34 Representation functions 11B37 Recurrences {For applications to special functions, see 33-XX} 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B50 Sequences (mod m) 11B57 Farey sequences; the sequences 1k , 2 k , . . . 11B65 Binomial coefficients; factorials; q-identities [See also 05A10, 05A30] 11B68 Bernoulli and Euler numbers and polynomials 11B73 Bell and Stirling numbers 11B75 Other combinatorial number theory 11B83 Special sequences and polynomials 11B85 Automata sequences 11B99 None of the above, but in this section |
11Bxx序列和集合 11B05密度、间隙、拓扑结构 11B13加法基，包括和集[另见 05B10] 11B25等差数列[另见11N13] 11B30算术组合学；高阶均匀性 11B34 表示函数 11B37重复项{用于特殊函数的应用程序， 参见33-XX} 11B39斐波那契数列、卢卡斯数列与多项式 以及泛化 11B50序列（模m） 11B57 Farey序列；序列1k , 2 k , . . . 11B65二项式系数；阶乘；q-恒等式[参见 也包括05A10、05A30] 11B68 Bernoulli数、Euler数和多项式 11B73 Bell数和Stirling数 11B75其他组合数论 11B83特殊序列和多项式 11B85自动机序列 11B99以上都不是，但本节适用 |
| 11Cxx Polynomials and matrices 11C08 Polynomials in number theory [See also 13F20] 11C20 Matrices, determinants in number theory [See also 15B36] 11C99 None of the above, but in this section |
11Cxx多项式和矩阵 11C08数论中的多项式[另见13F20] 11C20矩阵，数论中的行列式[另见15B36] 11C99以上均不符合，但本节适用 |
| 11Dxx Diophantine equations [See also 11Gxx, 14Gxx] 11D04 Linear Diophantine equations 11D07 The Frobenius problem 11D09 Quadratic and bilinear Diophantine equations 11D25 Cubic and quartic Diophantine equations 11D41 Higher degree equations; Fermat’s equation 11D45 Counting solutions of Diophantine equations 11D57 Multiplicative and norm form equations 11D59 Thue-Mahler equations 11D61 Exponential Diophantine equations 11D68 Rational numbers as sums of fractions 11D72 Diophantine equations in many variables [See also 11P55] 11D75 Diophantine inequalities [See also 11J25] 11D79 Congruences in many variables 11D85 Representation problems [See also 11P55] 11D88 p-adic and power series fields 11D99 None of the above, but in this section |
11Dxx丢番图方程[另见 11Gxx, 14Gxx] 11D04线性丢番图方程 11D07弗罗贝尼乌斯问题 11D09二次和双线性丢番图方程 11D25立方和四次丢番图方程 11D41高次方程；费马方程 11D45迪奥凡提安方程的计数解 11D57乘法和规范形式方程 11D59 Thue-Mahler方程 11D61指数型丢番图方程 11D68理想数作为分数之和 11D72多变量丢番图方程[另见11P55] 11D75 Diophantine不等式[另见11J25] 11D79许多变量的共线性 11D85代表性问题[另见11P55] 11D88 p进制和幂级数域 11D99以上均不符合，但本节适用 |
| 11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63} 11E04 Quadratic forms over general fields 11E08 Quadratic forms over local rings and fields 11E10 Forms over real fields 11E12 Quadratic forms over global rings and fields 11E16 General binary quadratic forms 11E20 General ternary and quaternary quadratic forms; forms of more than two variables 11E25 Sums of squares and representations by other particular quadratic forms 11E39 Bilinear and Hermitian forms 11E41 Class numbers of quadratic and Hermitian forms 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) 11E57 Classical groups [See also 14Lxx, 20Gxx] 11E70 K-theory of quadratic and Hermitian forms 11E72 Galois cohomology of linear algebraic groups [See also 20G10] 11E76 Forms of degree higher than two 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 11E88 Quadratic spaces; Clifford algebras [See also 15A63, 15A66] 11E95 p-adic theory 11E99 None of the above, but in this section |
11Exx表和线性代数群 [另见19Gxx]{关于二次型在 线性代数，参见15A63} 11E04一般域上的二次型 11E08局部环和域上的二次型 11E10实数域上的形式 11E12全域环与域上的二次型 11E16一般二元二次型 11E20一般三次和四次二次型；两个以上变量的二次型 11E25平方和与其它特定表示法 二次型 11E39双线性与埃尔米特形式 11E41二次型与埃尔米特型的类号 11E45分析理论（爱泼斯坦ζ函数；与自守形式及函数的关系） 11E57古代群体[另见14Lxx、20Gxx] 11E70二次型和埃尔米特型的K理论 11E72线性代数群的伽罗瓦上同调[另见20G10] 11E76二等以上学位 11E81二次型的代数理论；Witt群与环[另见19G12、19G24] 11E88二次空间；克利福德代数[另见15A63、15A66] 11E95 p进制理论 11E99以上均不符合，但本节适用 |
| 11Fxx Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 11F03 Modular and automorphic functions 11F06 Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 11F11 Holomorphic modular forms of integral weight 11F12 Automorphic forms, one variable 11F20 Dedekind eta function, Dedekind sums 11F22 Relationship to Lie algebras and finite simple groups 11F23 Relations with algebraic geometry and topology 11F25 Hecke-Petersson operators, differential operators (one variable) 11F27 Theta series; Weil representation; theta correspondences 11F30 Fourier coefficients of automorphic forms 11F32 Modular correspondences, etc. 11F33 Congruences for modular and p-adic modular forms [See also 14G20, 22E50] 11F37 Forms of half-integer weight; nonholomorphic modular forms 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F50 Jacobi forms 11F52 Modular forms associated to Drinfel’d modules 11F55 Other groups and their modular and automorphic forms (several variables) 11F60 Hecke-Petersson operators, differential operators (several variables) 11F66 Langlands L-functions; one variable Dirichlet series and functional equations 11F67 Special values of automorphic L-series, periods of automorphic forms, cohomology, modular symbols 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11F75 Cohomology of arithmetic groups 11F77 Automorphic forms and their relations with perfectoid spaces [See also 14G45] 11F80 Galois representations 11F85 p-adic theory, local fields [See also 14G20, 22E50] 11F99 None of the above, but in this section |
11Fxx不连续群与自同构形式[另见11R39、11S37、14Gxx、14Kxx、22E50、22E55、30F35、32Nxx]{关于二次型的关系，参见11E45} 11F03模块化和自形函数 11F06模块群和推广的结构；算术群[另见20H05、20H10、22E40] 11F11整权全纯模形式 11F12自形式，一个变量 11F20 Dedekind与函数，Dedekind和 11F22与李代数和有限单群的关系 11F23与代数几何和拓扑学的关系 11F25 Hecke-Petersson算子，微分算子（单变量） 11F27 Theta系列；韦尔表示法；theta对应关系 11F30自同形形式的傅里叶系数 11F32模块化对应等。 11F33模形式与p-进模形式的同调[另见14G20、22E50] 11F37半整数形式；非全纯模形式 11F41 GL(2)上的自同形形式；希尔伯特模群与希尔伯特-西格尔模群及其模形式与自同形形式；希尔伯特模曲面[另见14J20] 11F46 Siegel模群；Siegel和Hilbert-Siegel模形式与自守形式 11F50 Jacobi形式 11F52与Drinfel‘d模相关的模形式 11F55其他群体及其模块化与自形化形态（若干变量） 11F60 Hecke-Petersson算子，微分算子（多个变量） 11F66朗兰兹L函数；一个变量的狄利克雷级数和函数方程 11F67自同构L-系列的特殊值、自同构形式的周期、上同调、模符号 11F68与自守形式相关的若干复变量的狄利克雷级数；Weyl群多重狄利克雷级数 11F70表示论方法；局部和全局域上的自同态表示 11F72谱论；迹公式（例如Selberg公式） 11F75算术群的同调 11F77自同形形式及其与完美型空间的关系[另见14G45] 11F80伽罗瓦表示 11F85p-进理论，局部域[另见14G20,22E50] 11F99以上均不符合，但本节适用 |
| 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] 11G05 Elliptic curves over global fields [See also 14H52] 11G07 Elliptic curves over local fields [See also 14G20, 14H52] 11G09 Drinfel’d modules; higher-dimensional motives, etc. [See also 14L05] 11G10 Abelian varieties of dimension > 1 [See also 14Kxx] 11G15 Complex multiplication and moduli of abelian varieties [See also 14K22] 11G16 Elliptic and modular units [See also 11R27] 11G18 Arithmetic aspects of modular and Shimura varieties [See also 14G35] 11G20 Curves over finite and local fields [See also 14H25] 11G25 Varieties over finite and local fields [See also 14G15, 14G20] 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also 14H25] 11G32 Arithmetic aspects of dessins d’enfants, Bely˘ı theory 11G35 Varieties over global fields [See also 14G25] 11G40 L-functions of varieties over global fields; BirchSwinnerton-Dyer conjecture [See also 14G10] 11G42 Arithmetic mirror symmetry [See also 14J33] 11G45 Geometric class field theory [See also 11R37, 14C35, 19F05] 11G50 Heights [See also 14G40, 37P30] 11G55 Polylogarithms and relations with K-theory 11G99 None of the above, but in this section |
1Gxx算术代数几何（丢番图几何）[另见11Dxx、14Gxx、14Kxx] 11G05整体域上的椭圆曲线[另见14H52] 11G07局部域上的椭圆曲线[另见14G20、14H52] 11G09德林费尔德模；高维动机等[另见14L05] 11G10维数>的阿贝尔簇1[另见14Kxx] 11G15阿贝尔簇的复乘法与模结构[另见14K22] 11G16椭圆与模单位[另见11R27] 11G18模簇与志村簇的算术特性[另见14G35] 11G20有限域与局部域上的曲线[另见14H25] 11G25有限域与局部域上的簇[另见14G15,14G20] 11G30全域上任意亏格或亏格6=1的曲线[另见14H25]11G32儿童图的算术特性与Belyı理论11G35全域上的簇[另见14G25] 11G40全域簇的L函数与伯奇-斯温顿-戴尔猜想[另见14G10]11G42算术镜像对称性[另见14J33] 11G45几何类域论[另见11R37,14C35,19F05] 11G50高度理论[另见14G40,37P30] 11G55多重对数与K理论关系 11G99以上均不包含，但本节另见 |
| 11Hxx Geometry of numbers {For applications in coding theory, see 94B75} 11H06 Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07] 11H16 Nonconvex bodies 11H31 Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17] 11H46 Products of linear forms 11H50 Minima of forms 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11H56 Automorphism groups of lattices 11H60 Mean value and transfer theorems 11H71 Relations with coding theory 11H99 None of the above, but in this section |
11Hxx数论几何{编码理论应用参见94B75} 11H06晶格与凸体（数论方面）[另见11P21,52C05,52C07] 11H16非凸体11H31晶格堆积与覆盖（数论方面）[另见05B40,52C15,52C17] 11H46线性形式的乘积 11H50形式的极小值 11H55二次型（约化理论、极值形式等） 11H56晶格自同构群 11H60平均值定理与传递定理 11H71编码理论关系 11H99以上均不包含，但本节另见 |
| 11Jxx Diophantine approximation, transcendental number theory [See also 11K60] 11J04 Homogeneous approximation to one number 11J06 Markov and Lagrange spectra and generalizations 11J13 Simultaneous homogeneous approximation, linear forms 11J17 Approximation by numbers from a fixed field 11J20 Inhomogeneous linear forms 11J25 Diophantine inequalities [See also 11D75] 11J54 Small fractional parts of polynomials and generalizations 11J61 Approximation in non-Archimedean valuations 11J68 Approximation to algebraic numbers 11J70 Continued fractions and generalizations [See also 11A55, 11K50] 11J71 Distribution modulo one [See also 11K06] 11J72 Irrationality; linear independence over a field 11J81 Transcendence (general theory) 11J82 Measures of irrationality and of transcendence 11J83 Metric theory 11J85 Algebraic independence; Gel’fond’s method 11J86 Linear forms in logarithms; Baker’s method 11J87 Schmidt Subspace Theorem and applications 11J89 Transcendence theory of elliptic and abelian functions 11J91 Transcendence theory of other special functions 11J93 Transcendence theory of Drinfel’d and t-modules 15 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11J95 Results involving abelian varieties 11J97 Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) 11J99 None of the above, but in this section |
11Jxx迪奥芬茨逼近，超越数理论[另见11K60] |
| 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithms 11K06 General theory of distribution modulo 1 [See also 11J71] 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] 11K31 Special sequences 11K36 Well-distributed sequences and other variations 11K38 Irregularities of distribution, discrepancy [See also 11Nxx] 11K41 Continuous, p-adic and abstract analogues 11K45 Pseudo-random numbers; Monte Carlo methods [See also 65C05, 65C10] 11K50 Metric theory of continued fractions [See also 11A55, 11J70] 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx] 11K60 Diophantine approximation in probabilistic number theory [See also 11Jxx] 11K65 Arithmetic functions in probabilistic number theory [See also 11Nxx] 11K70 Harmonic analysis and almost periodicity in probabilistic number theory 11K99 None of the above, but in this section |
11Kxx概率论：模1分布；算法的度量理论 11K06模1分布的一般理论[另见11J71] 11K16正则数、进制展开、皮绍数、塞勒姆数、良格点等[另见11A63] 11K31特殊序列 11K36均匀分布序列及其他变体 11K38分布不规则性与差异[另见11Nxx] 11K41连续、p进制与抽象类比 11K45伪随机数；蒙特卡洛方法[另见65C05,65C10] 11K50连续分数的度量理论[另见11A55,11J70] 11K55其他算法与展开的度量理论；测度与豪斯多夫维数[另见11N99,28Dxx] 11K60概率数论中的丢番图逼近[另见11Jxx] 11K65概率数论中的算术函数[另见11Nxx] 11K70概率数论中的调和分析与几乎周期性 11K99以上均不适用，但本节 |
| 11Lxx Exponential sums and character sums {For finite fields, see 11Txx} 11L03 Trigonometric and exponential sums, general 11L05 Gauss and Kloosterman sums; generalizations 11L07 Estimates on exponential sums 11L10 Jacobsthal and Brewer sums; other complete character sums 11L15 Weyl sums 11L20 Sums over primes 11L26 Sums over arbitrary intervals 11L40 Estimates on character sums 11L99 None of the above, but in this section |
11Lxx指数和与特征和（有限域参见11Txx） 11L03三角和与指数和（通论） 11L05高斯和与克鲁斯特曼和（推广） 11L07指数和估计 11L10雅各布斯塔尔和与布鲁尔和（其他完整特征和） 11L15韦伊和 11L20素数和 11L26任意区间和 11L40特征和估计 11L99本节不涉及上述内容 |
| 11Mxx Zeta and L-functions: analytic theory 11M06 ζ(s) and L(s, χ) 11M20 Real zeros of L(s, χ); results on L(1, χ) 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheses 11M32 Multiple Dirichlet series and zeta functions and multizeta values 11M35 Hurwitz and Lerch zeta functions 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 11M38 Zeta and L-functions in characteristic p 11M41 Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10} [See also 11E45, 11F66, 11F70, 11F72] 11M45 Tauberian theorems [See also 40E05] 11M50 Relations with random matrices 11M55 Relations with noncommutative geometry 11M99 None of the above, but in this section |
11Mxxζ函数与L函数：解析理论 |
| 11Nxx Multiplicative number theory 11N05 Distribution of primes 11N13 Primes in congruence classes 11N25 Distribution of integers with specified multiplicative constraints 11N30 Tur´an theory [See also 30Bxx] 11N32 Primes represented by polynomials; other multiplicative structures of polynomial values 11N35 Sieves 11N36 Applications of sieve methods 11N37 Asymptotic results on arithmetic functions 16 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. 11N45 Asymptotic results on counting functions for algebraic and topological structures 11N56 Rate of growth of arithmetic functions 11N60 Distribution functions associated with additive and positive multiplicative functions 11N64 Other results on the distribution of values or the characterization of arithmetic functions 11N69 Distribution of integers in special residue classes 11N75 Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] 11N80 Generalized primes and integers 11N99 None of the above, but in this section |
11Nxx乘法数论 11N05素数分布 11N13同余类中的素数 11N25满足特定乘法约束的整数分布 11N30 Turán理论[另见30Bxx] 11N32多项式表示的素数其他多项式值的乘法结构 11N35筛选法 11N36筛选方法的应用 11N37算术函数的渐近结果16©2020《数学评论》与zbMATH。根据知识共享CC-BY-NC-SA许可协议发布。 11N45代数与拓扑结构计数函数的渐近结果 11N56算术函数的增长速率 11N60与加法及正乘法函数相关的分布函数 11N64关于值分布或算术函数特征的其他结果 11N69特殊剩余类中整数的分布 11N75自守函数与形式在乘法问题中的应用[另见11Fxx] 11N80广义素数与整数 11N99上述内容均不包含，但本节另列 |
| 11Pxx Additive number theory; partitions 11P05 Waring’s problem and variants 11P21 Lattice points in specified regions 11P32 Goldbach-type theorems; other additive questions involving primes 11P55 Applications of the Hardy-Littlewood method [See also 11D85] 11P70 Inverse problems of additive number theory, including sumsets 11P81 Elementary theory of partitions [See also 05A17] 11P82 Analytic theory of partitions 11P83 Partitions; congruences and congruential restrictions 11P84 Partition identities; identities of RogersRamanujan type 11P99 None of the above, but in this section |
11Pxx加法数论；划分 11P05沃林问题及其变体 11P21指定区域内的格点 11P32金巴赫型定理；涉及素数的其他加法问题 11P55哈代-利特尔伍德方法的应用[另见11D85] 11P70加法数论的逆问题，包括求和集11P81划分的初等理论[另见05A17] 11P82划分的解析理论 11P83划分；同余与同余限制 11P84划分恒等式；罗杰斯-拉马努金型恒等式 11P99上述内容均不包含，但本节另列 |
| 11Rxx Algebraic number theory: global fields {For complex multiplication, see 11G15} 11R04 Algebraic numbers; rings of algebraic integers 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11R09 Polynomials (irreducibility, etc.) 11R11 Quadratic extensions 11R16 Cubic and quartic extensions 11R18 Cyclotomic extensions 11R20 Other abelian and metabelian extensions 11R21 Other number fields 11R23 Iwasawa theory 11R27 Units and factorization 11R29 Class numbers, class groups, discriminants 11R32 Galois theory 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10] 11R34 Galois cohomology [See also 12Gxx, 19A31] 11R37 Class field theory 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] 11R42 Zeta functions and L-functions of number fields [See also 11M41, 19F27] 11R44 Distribution of prime ideals [See also 11N05] 11R45 Density theorems 11R47 Other analytic theory [See also 11Nxx] 11R52 Quaternion and other division algebras: arithmetic, zeta functions 11R54 Other algebras and orders, and their zeta and L-functions [See also 11S45, 16Hxx, 16Kxx] 11R56 Ad`ele rings and groups 11R58 Arithmetic theory of algebraic function fields [See also 14-XX] 11R59 Zeta functions and L-functions of function fields 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.) 11R65 Class groups and Picard groups of orders 11R70 K-theory of global fields [See also 19Fxx] 11R80 Totally real fields [See also 12J15] 11R99 None of the above, but in this section 17 © 2020 Mathematical Reviews and zbMATH. Published under a Creative Commons CC-BY-NC-SA license. |
11Rxx代数数论：整体域{复数乘法详见11G15} |
| 11Sxx Algebraic number theory: local and p-adic fields 11S05 Polynomials 11S15 Ramification and extension theory 11S20 Galois theory 11S23 Integral representations 11S25 Galois cohomology [See also 12Gxx, 16H05] 11S31 Class field theory; p-adic formal groups [See also 14L05] 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 11S40 Zeta functions and L-functions [See also 11M41, 19F27] 11S45 Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx] 11S70 K-theory of local fields [See also 19Fxx] 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.) 11S82 Non-Archimedean dynamical systems [See mainly 37Pxx] 11S85 Other nonanalytic theory 11S90 Prehomogeneous vector spaces 11S99 None of the above, but in this section |
11Sxx代数数论：局部域与p-进域 11S05多项式 11S15分歧与扩张理论 11S20戈尔瓦理论 11S23整数表示 11S25戈尔瓦上同调[另见12Gxx，16H05] 11S31类域论；p-进形式群[另见14L05] 11S37兰格兰兹-韦伊猜想，非阿贝尔类域论[另见11Fxx，22E50] 11S40ζ函数与L函数[另见11M41,19F27] 11S45代数与序及其ζ函数[另见11R52,11R54,16Hxx，16Kxx] 11S70局域域的K理论[另见19Fxx] 11S80其他解析理论（β函数与γ函数的类比、p-进积分等） 11S82非阿基米德动力系统[主要参见37Pxx] 11S85其他非解析理论11S90预齐次向量空间 11S99上述内容均不包含，但本节另设 |
| 11Txx Finite fields and commutative rings (number-theoretic aspects) 11T06 Polynomials over finite fields 11T22 Cyclotomy 11T23 Exponential sums 11T24 Other character sums and Gauss sums 11T30 Structure theory for finite fields and commutative rings (number-theoretic aspects) 11T55 Arithmetic theory of polynomial rings over finite fields 11T60 Finite upper half-planes 11T71 Algebraic coding theory; cryptography (numbertheoretic aspects) 11T99 None of the above, but in this section |
11Txx有限域与交换环（数论方面） 11T06有限域上的多项式 11T22循环分解 11T23指数和 11T24其他特征和与高斯和 11T30有限域与交换环的结构理论（数论方面） 11T55有限域上多项式环的算术理论 11T60有限上半平面 11T71代数编码理论；密码学（数论方面） 11T99以上均不适用，但本节适用 |
| 11Uxx Connections of number theory and logic 11U05 Decidability (number-theoretic aspects) [See also 03B25] 11U07 Ultraproducts (number-theoretic aspects) [See also 03C20] 11U09 Model theory (number-theoretic aspects) [See also 03Cxx] 11U10 Nonstandard arithmetic (number-theoretic aspects) [See also 03H15] 11U99 None of the above, but in this section |
11Uxx数论与逻辑的联系 11U05可判定性（数论方面）[另见03B25] 11U07超积（数论方面）[另见03C20] 11U09模型论（数论方面）[另见03Cxx] 11U10非标准算术（数论方面）[另见03H15] 11U99以上均不适用，但本节适用 |
| 11Yxx Computational number theory {For software etc., see 11-04} 11Y05 Factorization 11Y11 Primality 11Y16 Number-theoretic algorithms; complexity [See also 68Q25] 11Y35 Analytic computations 11Y40 Algebraic number theory computations 11Y50 Computer solution of Diophantine equations 11Y55 Calculation of integer sequences 11Y60 Evaluation of number-theoretic constants 11Y65 Continued fraction calculations (numbertheoretic aspects) 11Y70 Values of arithmetic functions; tables 11Y99 None of the above, but in this section |
11Yxx计算数论{软件等参见11-04} 11Y05因式分解 11Y11素数 11Y16数论算法；复杂度[另见68Q25] 11Y35分析计算 11Y40代数数论计算 11Y50迪奥凡提方程的计算机解法 11Y55整数序列的计算 11Y60评价数论常数 11Y65连续分数计算（数论方面） 11Y70算术函数和表格的数值 11Y99以上均不符合，但本节适用 |
| 11Zxx Miscellaneous applications of number theory 11Z05 Miscellaneous applications of number theory 11Z99 None of the above, but in this section |
11Zxx数论的其他应用 11Z05数论的其他应用 11Z99以上都不是，但本节适用 |
| 12-XX Field theory and polynomials 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory 12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory 12-02 Research exposition (monographs, survey articles) pertaining to field theory 12-03 History of field theory [Consider also classification numbers pertaining to Section 01] 12-04 Software, source code, etc. for problems pertaining to field theory 12-06 Proceedings, conferences, collections, etc. pertaining to field theory 12-08 Computational methods for problems pertaining to field theory 12-11 Research data for problems pertaining to field theory |
12-XX场论和多项式 12-00与场论相关的通用参考文献（手册、词典、参考书目等） 12-01与场论相关的入门性论述（教材、辅导论文等） 12-02与场论相关的研究论文（专著、综述文章） 12-03场论的历史[还应考虑与第01节相关的分类编号] 12-04与场论相关问题的软件、源代码等 12-06与场论相关的会议记录、会议、文集等 12-08场论问题的计算方法 12-11与场论有关的问题的研究数据 |
| 12Dxx Real and complex fields 12D05 Polynomials in real and complex fields: factorization 12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15} 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx] 12D99 None of the above, but in this section |
12Dxx实数和复数域 12D05实数域和复数域中的多项式：因式分解 12D10实数域与复数域中的多项式：零点位置（代数定理）{解析理论参见26C10、30C15} 12D15与平方和相关的域（形式上实域、毕达哥拉斯域等）[另见11Exx] 12D99以上都不是，但本节适用 |
| 12Exx General field theory 12E05 Polynomials in general fields (irreducibility, etc.) 12E10 Special polynomials in general fields 12E12 Equations in general fields 12E15 Skew fields, division rings [See also 11R52, 16Kxx] 12E20 Finite fields (field-theoretic aspects) 12E25 Hilbertian fields; Hilbert’s irreducibility theorem 12E30 Field arithmetic 12E99 None of the above, but in this section |
12Exx 一般场论 12E05一般域中的多项式（不可约性等） 12E10一般域中的特殊多项式 12E12一般场中的方程 12E15 偏斜场，除环[另见11R52,16Kxx] 12E20 有限域（域论方面） 12E25 希尔伯特域；希尔伯特不可约性定理 12E30现场算术 12E99以上均不符合，但本节适用 |
| 12Fxx Field extensions 12F05 Algebraic field extensions 12F10 Separable extensions, Galois theory 12F12 Inverse Galois theory 12F15 Inseparable field extensions 12F20 Transcendental field extensions 12F99 None of the above, but in this section |
12Fxx域扩展 12F05代数域扩张 12F10 可分离延拓，伽罗瓦理论 12F12逆伽罗瓦理论 12F15不可分的域扩张 12F20超越域扩张 12F99以上均不符合，但本节适用 |
| 12Gxx Homological methods (field theory) 12G05 Galois cohomology [See also 14F22, 16H05, 16K50] 12G10 Cohomological dimension of fields 12G99 None of the above, but in this section |
12Gxx同源法（场论） 12G05伽罗瓦上同调[另见14F22、16H05、16K50] 12G10场的同调维数 12G99以上都不是，但属于本节 |
|
12Hxx Differential and difference algebra
12H05Differential algebra [See also13Nxx] 12H10Difference algebra [See also39Axx]
12H20Abstract differential equations [See also34Mxx]
12H25p-adic differential equations [See also11S80,14G20] 12H99None of the above, but in this section |
12Hxx微分与差分代数 12H05微分代数[另见13Nxx] 12H10差分代数[另见39Axx] 12H20摘要微分方程[另见34Mxx] 12H25p-adic微分方程[另见11S80、14G20] 12H99以上都不是，但本节适用 |
| 12Jxx Topologicalfields 12J05Normedfields
12J10Valuedfields
12J12Formallyp-adicfields
12J15Orderedfields
12J17Topological semifields
12J20General valuation theory forfields [See also13A18]
12J25Non-Archimedean valuedfields [See also30G06,46S10]
12J27Krasner-Tate algebras [See mainly32P05; see also46S10,47S10]
12J99None of the above, but in this section |
12Jxx Topologicalfields 12J05Normedfields 12J10Valuedfields 12J12Formallyp-adicfields 12J15Orderedfields 12J17Topological semifields 12J20通用估值理论（适用于各领域）[另见13A18] 12J25非阿基米德赋值域[另见30G06、46S10] 12J27Krasner-Tate代数[参见32P05；另见46S10、47S10] 12J99以上都不是，但本节适用 |
| 12Kxx Generalizations offields 12K05Near-fields [See also16Y30] 12K10Semifields [See also16Y60]
12K99None of the above, but in this section
|
12Kxx 通用化场外 12K05近场[另见16Y30] 12K10半场[另见16Y60] 12K99以上都不是，但本节是 |
|
12Lxx Connections betweenfield theory and logic
12L05Decidability andfield theory [See also03B25] 12L10Ultraproducts andfield theory [See also03C20]
12L12Model theory offields [See also03C60]
12L15Nonstandard arithmetic andfield theory [See also03H15]
12L99None of the above, but in this section |
12Lxx场论与逻辑的联系 12L05可判定性与场论[另见03B25] 12L10超产品与场论[另见03C20] 12L12模型理论场外[另见03C60] 12L15非标准算术与域论[另见03H15] 12L99以上都不是，但本节适用 |
|
13-XX Commutative algebra
13-00General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra 13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra 13-02Research exposition (monographs, survey articles) pertaining to commutative algebra
13-03History of commutative algebra [Consider also classification numbers from Section01]
13-04Software, source code, etc. for problems pertaining to commutative algebra
13-06Proceedings, conferences, collections, etc. pertaining to commutative algebra
13-11Research data for problems pertaining to commutative algebra
|
13-XX交换代数 13-00交换代数相关的一般参考文献（手册、词典、参考书目等） 13-01 交换代数入门（教材、辅导资料等） 13-02交换代数相关研究论文（含专著、综述文章） 13-03交换代数史[另请参阅第01节的分类编号] 13-04交换代数相关问题的软件、源代码等 13-06交换代数相关的会议记录、会议、文集等 13-11交换代数相关问题的研究数据 |
|
13Axx General commutative ring theory
13A02 Graded rings [See also 16W50] 13A05 Divisibility and factorizations in commutative rings [See also 13F15] 13A15 Ideals and multiplicative ideal theory in commutative rings 13A18 Valuations and their generalizations for commutative rings [See also 12J20] 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 13A50 Actions of groups on commutative rings; invariant theory [See also 14L24] 13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) [See also 05C25, 05E40] 13A99 None of the above, but in this section |
13Axx一般交换环理论 |
| 13Bxx Commutative ring extensions and related topics 13B02 Extension theory of commutative rings 13B05 Galois theory and commutative ring extensions 13B10 Morphisms of commutative rings 13B21 Integral dependence in commutative rings; going up, going down 13B22 Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 13B25 Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] 13B30 Rings of fractions and localization for commutative rings [See also 16S85] 13B35 Completion of commutative rings [See also 13J10] 13B40 Etale and flat extensions; Henselization; Artin approximation [See also ´ 13J15,14B12, 14B25] 13B99 None of the above, but in this section |
13Bxx交换环扩张及相关课题 13B02交换环的扩张理论 13B05伽罗瓦理论与交换环扩张 13B10交换环的态射 13B21交换环中的整数依赖性；上升、下降 13B22 交换环与理想的整闭性[另见13A35]；整闭环、相关环（日语等） 13B25 交换环上的多项式[另见11C08、11T06、13F20、13M10] 13B30 交换环的分数环与局部化[另见16S85] 13B35交换环的完成[另见13J10] 13B40 展开与平坦延拓；Hensel化；Artin逼近[另见‘ 13J15,14B12, 14B25] 13B99以上都不是，但属于本节 |
| 13Cxx Theory of modules and ideals in commutative rings 13C05 Structure, classification theorems for modules and ideals in commutative rings 13C10 Projective and free modules and ideals in commutative rings [See also 19A13] 13C11 Injective and flat modules and ideals in commutative rings 13C12 Torsion modules and ideals in commutative rings 13C13 Other special types of modules and ideals in commutative rings 13C14 Cohen-Macaulay modules [See also 13H10] 13C15 Dimension theory, depth, related commutative rings (catenary, etc.) 13C20 Class groups [See also 11R29] 13C40 Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 13C60 Module categories and commutative rings 13C70 Theory of modules and ideals in commutative rings described by combinatorial properties [See also 05C25, 05E40] 13C99 None of the above, but in this section |
13Cxx交换环中的模与理想理论 13C05 交换环中模与理想的结构及分类定理 13C10 交换环中的射影模与自由模及理想[另见19A13] 13C11交换环中的注入模、平坦模与理想 13C12交换环中的扭模与理想 13C13交换环中的其他特殊类型的模与理想 13C14 Cohen-Macaulay模[另见13H10] 13C15 维度理论、深度、相关交换环（悬链线等） 13C20 群组[另见11R29] 13C40 连接、完全交集与行列式理想[另见14M06、14M10、14M12] 13C60模块分类与交换环 13C70 交换环中模与理想的理论，其性质由组合学特征描述[另见05C25、05E40] 13C99以上均不符合，但本节适用 |
| 13Dxx Homological methods in commutative ring theory {For noncommutative rings, see 16Exx; for general categories, see 18Gxx} 13D02 Syzygies, resolutions, complexes and commutative rings 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andr´e-Quillen, cyclic, dihedral, etc.) 13D05 Homological dimension and commutative rings 13D07 Homological functors on modules of commutative rings (Tor, Ext, etc.) 13D09 Derived categories and commutative rings 13D10 Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx] 13D15 Grothendieck groups, K-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] 13D22 Homological conjectures (intersection theorems) in commutative ring theory 13D30 Torsion theory for commutative rings [See also 13C12, 18E40] 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincar´e series 13D45 Local cohomology and commutative rings [See also 14B15] 13D99 None of the above, but in this section |
13Dxx 交换环理论中的同调方法 {非交换环参见16Exx；一般范畴参见18Gxx} 13D02合相、分解、复合体和交换环 13D03（交换环与代数的）同调（如霍希尔德、安德烈-基伦、循环、二面体等）； 13D05 同调维数与交换环 13D07 交换环模的同源函子（Tor、Ext等） 13D09派生范畴和交换环 13D10交换环理论中的变形与无穷小方法[另见14B10、14B12、14D15、32Gxx] 13D15 格罗滕迪克群、K理论与交换环[另见14C35、18F30、19Axx、19D50] 13D22 交换环论中的同调猜想（交集定理） 13D30交换环的扭理论[另见13C12、18E40] 13D40 希尔伯特-塞缪尔函数与希尔伯特-昆茨函数；庞加莱级数 13D45局部上同调与交换环[另见14B15] 13D99以上都不是，但本节如此 |
| 13Exx Chain conditions, finiteness conditions in commutative ring theory 13E05 Commutative Noetherian rings and modules 13E10 Commutative Artinian rings and modules, finite-dimensional algebras 13E15 Commutative rings and modules of finite generation or presentation; number of generators 13E99 None of the above, but in this section |
13Exx 交换环理论中的链条件与有限性条件 13E05交换诺特环与模 13E10 交换Artin环与模，有限维代数 13E15 交换环与有限生成或表示的模；生成元的数量 13E99以上都不是，但本节适用 |
| 13Fxx Arithmetic rings and other special commutative rings 13F05 Dedekind, Pr¨ufer, Krull and Mori rings and their generalizations 13F07 Euclidean rings and generalizations 13F10 Principal ideal rings 13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05] 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 13F25 Formal power series rings [See also 13J05] 13F30 Valuation rings [See also 13A18] 13F35 Witt vectors and related rings 13F40 Excellent rings 13F45 Seminormal rings 13F50 Rings with straightening laws, Hodge algebras 13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10] 13F60 Cluster algebras 13F65 Commutative rings defined by binomial ideals, toric rings, etc. [See also 14M25] 13F70 Other commutative rings defined by combinatorial properties 13F99 None of the above, but in this section |
13Fxx算术环及其他特殊交换环 13F05 Dedekind、Prüfer、Krull和Mori环及其推广 13F07欧几里得环与推广 13F10主理想环 13F15 由因式分解性质（如原子环、因子环、半因子环）定义的交换环[另见13A05、14M05] 13F20多项式环与理想；整数值多项式环[另见11C08、13B25] 13F25 正则幂级数环[另见13J05] 13F30 估值环[另见13A18] 13F35Witt向量和相关环 13F40 优质环 13F45半正常环 13F50具有正则化律的环，Hodge代数 13F55 由单项式理想定义的交换环；Stanley-Reisner 面环；单纯复形[另见 55U10] 13F60 簇代数 13F65 由二项式理想、环面环等定义的交换环[另见14M25] 13F70 其他由组合性质定义的交换环 13F99以上都不是，但本节如此 |
| 13Gxx Integral domains 13G05 Integral domains 13G99 None of the above, but in this section |
13Gxx 整数域 13G05积分域 13G99以上都不是，但本节适用 |
| 13Hxx Local rings and semilocal rings 13H05 Regular local rings 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13H15 Multiplicity theory and related topics [See also 14C17] 13H99 None of the above, but in this section |
13Hxx 本地环和半本地环 13H05常规本地环 13H10特殊类型（Cohen-Macaulay、Gorenstein、Buchsbaum等）[另见14M05] 13H15多重性理论及相关课题[另见14C17] 13H99以上都不是，但本节如此 |
| 13Jxx Topological rings and modules [See also 16W60, 16W80] 13J05 Power series rings [See also 13F25] 13J07 Analytical algebras and rings [See also 32B05] 13J10 Complete rings, completion [See also 13B35] 13J15 Henselian rings [See also 13B40] 13J20 Global topological rings 13J25 Ordered rings [See also 06F25] 13J30 Real algebra [See also 12D15, 14Pxx] 13J99 None of the above, but in this section |
13Jxx拓扑环与模[另见16W60、16W80] 13J05 功率系列环 [另见 13F25] 13J07 分析代数和环[另见32B05] 13J10 完整的环，完成[另见13B35] 13J15 Henselian环[另见13B40] 13J20 全球拓扑环 13J25有序环[另见06F25] 13J30 实代数[另见12D15、14Pxx] 13J99以上都不是，但本节是 |
| 13Lxx Applications of logic to commutative algebra [See also 03Cxx, 03Hxx] 13L05 Applications of logic to commutative algebra [See also 03Cxx, 03Hxx] 13L99 None of the above, but in this section |
13Lxx 逻辑在交换代数中的应用[另见03Cxx、03Hxx] 13L05 逻辑在交换代数中的应用[另见03Cxx、03Hxx] 13L99 以上均不适用，但本节另设 |
| 13Mxx Finite commutative rings {For number-theoretic aspects, see 11Txx} 13M05 Structure of finite commutative rings 13M10 Polynomials and finite commutative rings 13M99 None of the above, but in this section |
13Mxx 有限交换环{关于数论方面的内容，参见11Txx} 13M05 有限交换环的结构13M10 多项式与有限交换环13M99 以上均不适用，但本节另设 |
| 13Nxx Differential algebra [See also 12H05, 14F10] 13N05 Modules of differentials 13N10 Commutative rings of differential operators and their modules [See also 16S32, 32C38] 13N15 Derivations and commutative rings 13N99 None of the above, but in this section |
13Nxx 微分代数[另见12H05、14F10] 13N05 微分模 13N10 微分算子的交换环及其模[另见16S32、32C38] 13N15 导数与交换环 13N99 以上均不适用，但本节另设 |
| 13Pxx Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] {For software etc., see 13-04} 13P05 Polynomials, factorization in commutative rings [See also 12-08] 13P10 Gr¨obner bases; other bases for ideals and modules (e.g., Janet and border bases) 13P15 Solving polynomial systems; resultants 13P20 Computational homological algebra [See also 13Dxx] 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 13P99 None of the above, but in this section |
13Pxx 交换环的计算方面与应用[另见14Qxx、68W30] {关于软件等，参见13-04} 13P05 多项式在交换环中的因式分解[另见12-08] 13P10 格雷伯纳基；理想与模的其他基（如珍妮特基和边界基） 13P15 多项式系统的求解；结果式 13P20 计算同调代数[另见13Dxx] 13P25 交换代数的应用（如统计学、控制论、优化等）13P99 以上均不适用，但本节另设 |
| 14-XX Algebraic geometry 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry 14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry 14-03 History of algebraic geometry [Consider also classification numbers from Section 01] 14-04 Software, source code, etc. for problems pertaining to algebraic geometry 14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry 14-11 Research data for problems pertaining to algebraic geometry |
14-XX代数几何 14-00 代数几何相关的一般参考文献（手册、词典、参考书目等） 14-01 代数几何相关入门性论述（教材、辅导论文等） 14-02 代数几何相关研究论文（包括专著、综述性文章） 14-03 代数几何史[另请参阅第01节的分类编号] 14-04代数几何相关问题的软件、源代码等 14-06 代数几何相关的会议记录、会议、文集等 14-11代数几何问题的研究数据 |
| 14Axx Foundations of algebraic geometry 14A05 Relevant commutative algebra [See also 13-XX] 14A10 Varieties and morphisms 14A15 Schemes and morphisms 14A20 Generalizations (algebraic spaces, stacks) 14A21 Logarithmic algebraic geometry, log schemes 14A22 Noncommutative algebraic geometry [See also 16S38] 14A23 Geometry over the field with one element 14A25 Elementary questions in algebraic geometry 14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} 14A99 None of the above, but in this section |
14Axx代数几何基础 14A05 相关交换代数[另见13-XX] 14A10 品种和态射 14A15 方案和态射 14A20推广（代数空间、堆栈） 14A21对数代数几何，对数概形 14A22非交换代数几何[另见16S38] 14A23 一个元素的域上的几何 14A25代数几何基础问题 14A30 代数几何中的基本构造，涉及高阶范畴与导出范畴（同伦代数几何、导出代数几何等）{分类相关方面参见18Fxx、18Gxx} 14A99以上都不是，但属于本节 |
| 14Bxx Local theory in algebraic geometry 14B05 Singularities in algebraic geometry [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14B07 Deformations of singularities [See also 14D15, 32S30] 14B10 Infinitesimal methods in algebraic geometry [See also 13D10] 14B12 Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 14B15 Local cohomology and algebraic geometry [See also 13D45, 32C36] 14B20 Formal neighborhoods in algebraic geometry 14B25 Local structure of morphisms in algebraic geometry: ´etale, flat, etc. [See also 13B40] 14B99 None of the above, but in this section |
14Bxx代数几何中的局部理论 14B05 代数几何中的奇点[另见14E15、14H20、14J17、32Sxx、58Kxx] 14B07 奇点的变形[另见14D15、32S30] 14B10 代数几何中的无穷小方法[另见13D10] 14B12局部变形理论、Artin近似等[另见13B40、13D10] 14B15局部上同调与代数几何[另见13D45、32C36] 14B20代数几何中的正规邻域 14B25 代数几何中态射的局部结构：étale、平坦等[另见13B40] 14B99以上都不是，但属于本节 |
| 14Cxx Cycles and subschemes 14C05 Parametrization (Chow and Hilbert schemes) 14C15 (Equivariant) Chow groups and rings; motives 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15] 14C20 Divisors, linear systems, invertible sheaves 14C21 Pencils, nets, webs in algebraic geometry [See also 53A60] 14C22 Picard groups 14C25 Algebraic cycles 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35, 58A14], Hodge conjecture 14C34 Torelli problem [See also 32G20] 14C35 Applications of methods of algebraic K-theory in algebraic geometry [See also 19Exx] 14C40 Riemann-Roch theorems [See also 19E20, 19L10] 14C99 None of the above, but in this section |
14Cxx循环和子方案 |
| 14Dxx Families, fibrations in algebraic geometry 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 14D06 Fibrations, degenerations in algebraic geometry 14D07 Variation of Hodge structures (algebro-geometric aspects) [See also 32G20] 14D10 Arithmetic ground fields (finite, local, global) and families or fibrations 14D15 Formal methods and deformations in algebraic geometry [See also 13D10, 14B07, 32Gxx] 14D20 Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] 14D22 Fine and coarse moduli spaces 14D23 Stacks and moduli problems 14D24 Geometric Langlands program (algebro-geometric aspects) [See also 22E57] 14D99 None of the above, but in this section |
14Dxx 家族理论，代数几何中的纤维化 14D05 家族结构（皮卡-莱夫谢茨理论、单值性等）14D06 纤维化与代数几何中的退化 14D07 霍奇结构的变化（代数几何方面）[另见32G20] 14D10 算术基域（有限域、局部域、整体域）及其对应家族或纤维化 14D15 代数几何中的形式方法与形变[另见13D10、14B07、32Gxx] 14D20 代数模问题与向量丛模空间{解析模问题参见32G13} 14D21 向量丛与模空间在数学物理中的应用（扭量理论、瞬子、量子场论）[另见32L25、81Txx] 14D22 精细模空间与粗略模空间 14D23 堆栈与模问题 14D24 几何朗兰兹纲领（代数几何方面）[另见22E57] 14D99 上述内容均不涉及，但本节包含 |
| 14Exx Birational geometry 14E05 Rational and birational maps 14E07 Birational automorphisms, Cremona group and generalizations 14E08 Rationality questions in algebraic geometry [See also 14M20] 14E15 Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45] 14E16 McKay correspondence 14E18 Arcs and motivic integration 14E20 Coverings in algebraic geometry [See also 14H30] 14E22 Ramification problems in algebraic geometry [See also 11S15] 14E25 Embeddings in algebraic geometry 14E30 Minimal model program (Mori theory, extremal rays) 14E99 None of the above, but in this section |
14Exx 双有理几何 14E05 理性映射与双有理映射 14E07 双有理自同构、克雷莫纳群及其推广 14E08 代数几何中的有理性问题[另见14M20] 14E15 全局理论与奇点解析（代数几何方面）[另见14B05、32S20、32S45] 14E16 麦凯对应 14E18 弧与动机积分 14E20 代数几何中的覆盖理论[另见14H30] 14E22 代数几何中的分歧问题[另见11S15] 14E25 代数几何中的嵌入理论 14E30 最小模型纲领（森理论、极射理论） 14E99 上述内容均不涉及，但本节包含 |
| 14Fxx (Co)homology theory in algebraic geometry [See also 13Dxx] 14F06 Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32L10, 46M20] 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx] 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 14F17 Vanishing theorems in algebraic geometry [See also 32L20] 14F18 Multiplier ideals 14F20 Etale and other Grothendieck topologies and (co)homologies ´ 14F22 Brauer groups of schemes [See also 12G05, 16K50] 14F25 Classical real and complex (co)homology in algebraic geometry 14F30 p-adic cohomology, crystalline cohomology 14F35 Homotopy theory and fundamental groups in algebraic geometry [See also 14H30] 14F40 de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10] 14F42 Motivic cohomology; motivic homotopy theory [See also 19E15] 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14F45 Topological properties in algebraic geometry 14F99 None of the above, but in this section |
14Fxx代数几何中的（Co）同源理论[另见13Dxx] 14F06 代数几何中的链环 [另见 14F08、14H60、14J60、18F20、32L10、46M20] 14F08 短射的导出范畴、dg范畴及相关构造在代数几何中的应用[另见14A30、14F06、18Gxx] 14F10微分簇及其他特殊簇；D-模；Bernstein-Sato理想与多项式[另见13Nxx、32C38] 14F17 代数几何中的消失定理[另见32L20] 14F18乘数理想 14F20 展示板及其他格罗滕迪克拓扑与（上）同调 14F22概型的Brauer群[另见12G05、16K50] 14F25代数几何中的经典实与复（上）同调 14F30p进制上同调，晶体上同调 14F35 同伦论与代数几何中的基本群[另见14H30] 14F40 德·拉姆上同调与代数几何[另见14C30、32C35、32L10] 14F42 动机上同调；动机同伦理论[另见19E15] 14F43 其他代数几何（上）同调（如交上同调、等变上同调、劳森上同调、德利涅上同调） 14F45代数几何中的拓扑性质 14F99以上均不符合，但本节适用 |
| 14Gxx Arithmetic problems in algebraic geometry; Diophantine geometry [See also 11Dxx, 11Gxx] 14G05 Rational points 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40] 14G12 Hasse principle, weak and strong approximation, Brauer-Manin obstruction [See also 14F22] 14G15 Finite ground fields in algebraic geometry 14G17 Positive characteristic ground fields in algebraic geometry 14G20 Local ground fields in algebraic geometry 14G22 Rigid analytic geometry 14G25 Global ground fields in algebraic geometry 14G27 Other nonalgebraically closed ground fields in algebraic geometry 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) 14G35 Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] 14G45 Perfectoid spaces and mixed characteristic 14G50 Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40] 14G99 None of the above, but in this section |
14Gxx 代数几何中的算术问题；丢番图几何[另见11Dxx、11Gxx] 14G05有理点 14G10 Zeta函数与代数几何相关问题（如Birch-Swinnerton-Dyer猜想）[另见11G40] 14G12哈塞原理、弱逼近与强逼近、布劳尔-马宁障碍（另见14F22） 14G15代数几何中的有限地面场 代数几何中的 14G17正特征基底场 14G20代数几何中的局部地面场 14G22刚性解析几何 代数几何中的 14G25全球地面场 14G27 代数几何中其他非代数闭基域 14G32 万有群（与模空间的关系、射影群与模塔、伽罗瓦理论） 14G35模块化和Shimura品种[另见11F41、11F46、11G18] 14G40算术簇与概形；Arakelov理论；高度[另见11G50、37P30] 14G45完美空间与混合特征 14G50 算术几何的编码理论与密码学应用[另见94A60、94B27、94B40] 14G99以上都不是，但属于本节 |
|
14Hxx Curves in algebraic geometry |
14Hxx代数几何中的曲线 14H05 代数几何中的代数函数与函数域[另见11R58] 14H10 家族，曲线模（代数） 14H15 家族，曲线模块（解析）[另见30F10、32G15] 14H20 曲线奇点，局部环[另见13Hxx，14B05] 14H25 曲线的算术基域[另见11Dxx、11G05、14Gxx] 14H30 曲线的覆盖，基本群[另见14E20,14F35] 14H37 曲线自同构 14H40 雅可比簇、普赖姆簇[另见32G20] 14H42 Theta函数和曲线；Schottky问题[另见14K25,32G20] 14H45特殊代数曲线和低亏格曲线 14H50 平面曲线与空间曲线 14H51 曲线上特殊除子（亏格、Brill-Noether理论） 14H52 椭圆曲线[另见11G05、11G07、14Kxx] 14H55黎曼曲面；魏尔斯特拉斯点；间隙序列[另见30Fxx] 14H57 儿童绘画理论 {算术方面请参见11G32} 曲线上的14H60向量丛及其模空间[另见14D20、14F06、14J60] 14H70代数曲线与可积系统的关系 14H81代数曲线与物理学的关系 14H99以上都不是，但本节如此 |
| 14Jxx Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx} 14J10 Families, moduli, classification: algebraic theory 14J15 Moduli, classification: analytic theory; relations with modular forms [See also 32G13] 14J17 Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25] 14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx] 14J25 Special surfaces {For Hilbert modular surfaces, see 14G35} 14J26 Rational and ruled surfaces 14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations 14J28 K3 surfaces and Enriques surfaces 14J29 Surfaces of general type 14J30 3-folds 14J32 Calabi-Yau manifolds (algebro-geometric aspects) [See also 32Q25] 14J33 Mirror symmetry (algebro-geometric aspects) [See also 11G42, 53D37] 14J35 4-folds 14J40 n-folds (n > 4) 14J42 Holomorphic symplectic varieties, hyper-K¨ahler varieties 14J45 Fano varieties 14J50 Automorphisms of surfaces and higher-dimensional varieties 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx] 14J70 Hypersurfaces and algebraic geometry 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) 14J81 Relationships between surfaces, higher-dimensional varieties, and physics 14J99 None of the above, but in this section |
14Jxx 曲面与高维流形（解析理论参见32Jxx） 14J10 家族、模、分类：代数理论 14J15 模块，分类：解析理论；与模形式的关系[另见32G13] 14J17 曲面或高维簇的奇点[另见14B05、14E15、32S05、32S25] 14J20 表面或高维簇的算术基域[另见11Dxx、11G25、11G35、14Gxx] 14J25 特殊曲面（希尔伯特模曲面参见14G35） 14J26 理想曲面与规则曲面 14J27 椭圆曲面，椭圆或卡拉比-丘纤维化 14J28 K3曲面和恩里克斯曲面 14J29一般型曲面 14J30 3倍 14J32 卡拉比-丘流形（代数几何方面）[另见32Q25] 14J33镜像对称（代数几何方面）[另见11G42、53D37] 14J35 4重态 14J40 n重态（n > 4） 14J42 全纯辛流形与超凯勒流形 14J45 Fano 品种 14J50曲面与高维簇的自同构 14J60 曲面与高维簇上的向量丛及其模空间[另见14D20、14F06、14H60、32Lxx] 14J70超曲面与代数几何 14J80 表面拓扑（唐纳森多项式、塞伯格-威滕不变量） 14J81表面、高维品种与物理学之间的关系 14J99以上都不是，但本节是 |
| 14Kxx Abelian varieties and schemes 14K02 Isogeny 14K05 Algebraic theory of abelian varieties 14K10 Algebraic moduli of abelian varieties, classification [See also 11G15] 14K12 Subvarieties of abelian varieties 14K15 Arithmetic ground fields for abelian varieties [See also 11Dxx, 11Fxx, 11G10, 14Gxx] 14K20 Analytic theory of abelian varieties; abelian integrals and differentials 14K22 Complex multiplication and abelian varieties [See also 11G15] 14K25 Theta functions and abelian varieties [See also 14H42] 14K30 Picard schemes, higher Jacobians [See also 14H40, 32G20] 14K99 None of the above, but in this section |
14Kxx阿贝尔簇与概形 14K02同源性 14K05阿贝尔簇的代数理论 14K10阿贝尔簇的代数模，分类[另见11G15] 14K12阿贝尔簇的子簇 14K15阿贝尔簇的算术基域[另见11Dxx、11Fxx、11G10、14Gxx] 14K20阿贝尔簇的解析理论；阿贝尔积分与微分 14K22 复乘法与阿贝尔簇[另见11G15] 14K25 Theta函数与阿贝尔簇[另见14H42] 14K30 Picard方案，高雅可比安[另见14H40,32G20] 14K99以上都不是，但本节是 |
| 14Lxx Algebraic groups [See also 11E57] {For Lie algebras, see 17B45; for linear algebraic groups, see 20Gxx} 14L05 Formal groups, p-divisible groups [See also 55N22] 14L10 Group varieties 14L15 Group schemes 14L17 Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18C40] 14L24 Geometric invariant theory [See also 13A50] 14L30 Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14L35 Classical groups (algebro-geometric aspects) [See also 20Gxx, 51N30] 14L40 Other algebraic groups (geometric aspects) 14L99 None of the above, but in this section |
14Lxx 代数群[另见11E57] {关于李代数，参见17B45；关于线性代数群，参见20Gxx} 14L05正规群，p可除群[另见55N22] 14L10组品种 14L15集团方案 14L17仿射代数群，超代数构造[另见17B45、18C40] 14L24几何不变量理论[另见13A50] 14L30 品种或模式（商）的群作用[另见13A50、14L24、14M17] 14L35古典群（代数几何方面）[另见20Gxx、51N30] 14L40 其他代数群（几何方面） 14L99以上都不是，但本节适用 |
| 14Mxx Special varieties 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] 14M06 Linkage [See also 13C40] 14M07 Low codimension problems in algebraic geometry 14M10 Complete intersections [See also 13C40] 14M12 Determinantal varieties [See also 13C40] 14M15 Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M17 Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] 14M20 Rational and unirational varieties [See also 14E08] 14M22 Rationally connected varieties 14M25 Toric varieties, Newton polyhedra, Okounkov bodies [See also 52B20] 14M27 Compactifications; symmetric and spherical varieties 14M30 Supervarieties [See also 32C11, 58A50] 14M35 Character varieties 14M99 None of the above, but in this section |
14Mxx特殊品种 14M05 由环条件（因子环、Cohen-Macaulay环、半正规环）定义的品种[另见13F15、13F45、13H10] 14M06 Linkage[另见13C40] 代数几何中的 14M07低余维问题 14M10完全交叉[另见13C40] 14M12行列式簇[另见13C40] 14M15 格拉斯曼流形、舒伯特簇、旗流形[另见32M10、51M35] 14M17 均匀空间与推广[另见32M10、53C30、57T15] 14M20 理性与单有理簇[另见14E08] 14M22 理性连通簇 14M25 环面簇、牛顿多面体、奥孔科夫体[另见52B20] 14M27 紧凑化；对称与球面簇 14M30 超簇 [另见 32C11,58A50] 14M35 特征簇 14M99 上述均不适用，但本节 |
| 14Nxx Projective and enumerative algebraic geometry [See also 51-XX] 14N05 Projective techniques in algebraic geometry [See also 51N35] 14N07 Secant varieties, tensor rank, varieties of sums of powers 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14N15 Classical problems, Schubert calculus 14N20 Configurations and arrangements of linear subspaces 14N25 Varieties of low degree 14N30 Adjunction problems 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45] 14N99 None of the above, but in this section |
14Nxx射影与枚举代数几何[另见51-XX] 14N05 投影技术在代数几何中的应用[另见51N35] 14N07 正割曲线族，张量秩，幂和曲线族 14N10 代数几何中的枚举问题（组合问题） 14N15经典问题，舒伯特微积分 14N20 线性子空间的配置与排列 14N25低度品种 14N30连接问题 14N35 格罗莫夫-维滕不变量、量子上同调、戈帕库马尔-瓦法不变量、唐纳森-托马斯不变量（代数几何方面）[另见53D45] 14N99以上都不是，但本节如此 |
| 14Pxx Real algebraic and real-analytic geometry 14P05 Real algebraic sets [See also 12D15, 13J30] 14P10 Semialgebraic sets and related spaces 14P15 Real-analytic and semi-analytic sets [See also 32B20, 32C05] 14P20 Nash functions and manifolds [See also 32C07, 58A07] 14P25 Topology of real algebraic varieties 14P99 None of the above, but in this section |
14Pxx实代数与实解析几何 14P05实代数集[另见12D15、13J30] 14P10半代数集及相关空间 14P15实解析集与半解析集[另见32B20、32C05] 14P20 Nash函数与流形[另见32C07、58A07] 14P25实代数簇的拓扑结构 14P99以上都不是，但本节如此 |
| 14Qxx Computational aspects in algebraic geometry {For software etc., see 14-04} [See also 12-08, 13Pxx, 68W30] 14Q05 Computational aspects of algebraic curves [See also 14Hxx] 14Q10 Computational aspects of algebraic surfaces [See also 14Jxx] 14Q15 Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx] 14Q20 Effectivity, complexity and computational aspects of algebraic geometry 14Q25 Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] 14Q30 Computational real algebraic geometry [See also 14Pxx] 14Q65 Geometric aspects of numerical algebraic geometry [See also 65H14] 14Q99 None of the above, but in this section |
14Qxx代数几何中的计算方面{对于软件等，请参见14-04} [另请参见12-08、13Pxx、68W30] 14Q05 代数曲线的计算方面[另见14Hxx] 14Q10代数曲面的计算方面[另见14Jxx] 14Q15高维簇的计算方面[另见14Jxx、14Mxx] 14Q20代数几何的有效性、复杂性和计算方面 14Q25算术基域上的计算代数几何[另见14Gxx、14H25、14Kxx] 14Q30 计算实代数几何[另见14Pxx] 14Q65 数值代数几何的几何方面[另见65H14] 14Q99以上都不是，但本节是 |
| 14Rxx Affine geometry 14R05 Classification of affine varieties 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R15 Jacobian problem [See also 13F20] 14R20 Group actions on affine varieties [See also 13A50, 14L30] 14R25 Affine fibrations [See also 14D06] 14R99 None of the above, but in this section |
14Rxx Affine geometry 14R05仿射簇的分类 14R10仿射空间（自同构、嵌入、奇异结构、消去问题） 14R15 Jacobian问题[另见13F20] 14R20仿射簇上的群作用[另见13A50、14L30] 14R25 Affine纤维化[另请参见14D06] 14R99以上都不是，但本节适用 |
| 14Txx Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14T10 Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} 14T15 Combinatorial aspects of tropical varieties 14T20 Geometric aspects of tropical varieties 14T25 Arithmetic aspects of tropical varieties 14T90 Applications of tropical geometry 14T99 None of the above, but in this section |
14Txx热带几何[另见12K10、14M25、14N10、52B20] 14T10 热带几何基础及其与代数的关系 {代数方面参见 15A80} 14T15热带品种的组合方面 14T20 热带品种的几何方面 14T25热带品种的算术方面 14T90热带几何的应用 14T99以上都不是，但本节如此 |
| 15-XX Linear and multilinear algebra; matrix theory 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to linear algebra 15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra 15-02 Research exposition (monographs, survey articles) pertaining to linear algebra 15-03 History of linear algebra [Consider also classification numbers from Section 01] 15-04 Software, source code, etc. for problems pertaining to linear algebra 15-06 Proceedings, conferences, collections, etc. pertaining to linear algebra 15-11 Research data for problems pertaining to linear algebra |
15-XX线性与多元线性代数；矩阵理论 15-00 线性代数相关的一般参考文献（手册、词典、参考书目等） 15-01 线性代数入门（教材、辅导资料等） 15-02 线性代数相关研究论文（包括专著、综述性文章） 15-03 线性代数史[另请参阅第01节的分类编号] 15-04与线性代数相关问题的软件、源代码等 15-06 与线性代数相关的会议记录、会议、文集等 15-11 线性代数相关问题的研究数据 |
| 15Axx Basic linear algebra 15A03 Vector spaces, linear dependence, rank, lineability 15A04 Linear transformations, semilinear transformations 15A06 Linear equations (linear algebraic aspects) 15A09 Theory of matrix inversion and generalized inverses 15A10 Applications of generalized inverses 15A12 Conditioning of matrices [See also 65F35] 15A15 Determinants, permanents, traces, other special matrix functions [See also 19B10, 19B14] 15A16 Matrix exponential and similar functions of matrices 15A18 Eigenvalues, singular values, and eigenvectors 15A20 Diagonalization, Jordan forms 15A21 Canonical forms, reductions, classification 15A22 Matrix pencils [See also 47A56] 15A23 Factorization of matrices 15A24 Matrix equations and identities 15A27 Commutativity of matrices 15A29 Inverse problems in linear algebra 15A30 Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx] 15A39 Linear inequalities of matrices 15A42 Inequalities involving eigenvalues and eigenvectors 15A45 Miscellaneous inequalities involving matrices 15A54 Matrices over function rings in one or more variables 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx] 15A66 Clifford algebras, spinors 15A67 Applications of Clifford algebras to physics, etc. 15A69 Multilinear algebra, tensor calculus 15A72 Vector and tensor algebra, theory of invariants [See also 13A50, 14L24] 15A75 Exterior algebra, Grassmann algebras 15A78 Other algebras built from modules 15A80 Max-plus and related algebras 15A83 Matrix completion problems 15A86 Linear preserver problems 15A99 None of the above, but in this section |
15Axx 基础线性代数 15A03 向量空间、线性相关性、秩、线性可导性 15A04 线性变换、半线性变换 15A06 线性方程（线性代数方面） 15A09 矩阵求逆与广义逆理论 15A10 广义逆的应用 15A12 矩阵条件化[另见65F35] 15A15 行列式、永久式、迹及其他特殊矩阵函数[另见19B10,19B14] 15A16 矩阵指数与矩阵类似函数 15A18 特征值、奇异值与特征向量 15A20 对角化、约旦标准型 15A21 标准型、约化与分类 15A22 矩阵铅笔[另见47A56] 15A23 矩阵分解 15A24 矩阵方程与恒等式 15A27 矩阵交换性 15A29 线性代数中的逆问题 15A30 矩阵代数系统[另见16S50,20Gxx，20Hxx] 15A39 矩阵线性不等式 15A42 特征值与特征向量相关不等式 15A45 矩阵相关各类不等式 15A54 一元或多变量函数环上的矩阵 15A60 矩阵范数、数值范围、泛函分析在矩阵理论中的应用[另见65F35,65J05] 15A63 二次型与双线性形式、内积[主要参见11Exx] 15A66 克利福德代数、旋量 15A67 克利福德代数在物理等领域的应用 15A69 多线性代数、张量微积分 15A72 矢量与张量代数、不变量理论[另见13A50,14L24] 15A75 外代数Grassmann代数 15A78 由模构建的其他代数 15A80 Max-plus及相关代数 15A83 矩阵补全问题 15A86 线性保持问题 15A99 以上均不适用，但本节 |
| 15Bxx Special matrices 15B05 Toeplitz, Cauchy, and related matrices 15B10 Orthogonal matrices 15B15 Fuzzy matrices 15B30 Matrix Lie algebras 15B33 Matrices over special rings (quaternions, finite fields, etc.) 15B34 Boolean and Hadamard matrices 15B35 Sign pattern matrices 15B36 Matrices of integers [See also 11C20] 15B48 Positive matrices and their generalizations; cones of matrices 15B51 Stochastic matrices 15B52 Random matrices (algebraic aspects) {For probabilistic aspects, see 60B20} 15B57 Hermitian, skew-Hermitian, and related matrices 15B99 None of the above, but in this section |
15Bxx 特殊矩阵 15B05 Toeplitz、柯西及相关矩阵 15B10 正交矩阵 15B15 模糊矩阵 15B30 矩阵李代数 15B33 特殊环（如四元数、有限域等）上的矩阵 15B34布尔矩阵和Hadamard矩阵 15B35 签名模式矩阵 15B36 整数矩阵[另见11C20] 15B48 正矩阵及其推广；矩阵锥 15B51 随机矩阵 15B52 随机矩阵（代数方面）{关于概率方面，参见60B20} 15B57埃尔米特矩阵、斜埃尔米特矩阵及相关矩阵 15B99以上都不是，但属于本节 |
| 16-XX Associative rings and algebras {For the commutative case, see 13-XX} 16-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras 16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras 16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras 16-03 History of associative rings and algebras [Consider also classification numbers from Section 01] 16-04 Software, source code, etc. for problems pertaining to associative rings and algebras 16-06 Proceedings, conferences, collections, etc. pertaining to associative rings and algebras 16-11 Research data for problems pertaining to associative rings and algebras |
16-XX 交换环与代数 {交换环的详细信息请参见13-XX} 16-00 关于关联环与代数的通用参考文献（手册、词典、参考书目等） 16-01 关于结合环与代数的入门性论述（教材、辅导论文等） 16-02 关于关联环与代数的研究论文（包括专著、综述文章） 16-03 关联环与代数的历史[另请参阅第01节的分类编号] 16-04 关于关联环和代数问题的软件、源代码等 16-06 与关联环和代数相关的会议记录、会议、文集等 16-11 关于关联环与代数问题的研究数据 |
| 16Bxx General and miscellaneous 16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18-XX] 16B70 Applications of logic in associative algebras [See also 03Cxx] 16B99 None of the above, but in this section |
16Bxx一般和杂项 16B50 联合代数中的范畴论方法和结果（除16D90外）[另见18-XX] 16B70 逻辑在结合代数中的应用[另见03Cxx] 16B99以上都不是，但属于本节 |
| 16Dxx Modules, bimodules and ideals in associative algebras 16D10 General module theory in associative algebras 16D20 Bimodules in associative algebras 16D25 Ideals in associative algebras 16D30 Infinite-dimensional simple rings (except as in 16Kxx) 16D40 Free, projective, and flat modules and ideals in associative algebras [See also 19A13] 16D50 Injective modules, self-injective associative rings [See also 16L60] 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras 16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 16D80 Other classes of modules and ideals in associative algebras [See also 16G50] 16D90 Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 16D99 None of the above, but in this section |
16Dxx模、双模与关联代数中的理想 16D10 关联代数中的一般模理论 16D20关联代数中的双模 16D25关联代数中的理想 16D30无限维简单环（16Kxx除外） 16D40 关联代数中的自由、投射和平面模与理想[另见19A13] 16D50 注射式模块，自注入式关联环[另见16L60] 16D60 单模与半单模、原始环及理想在结合代数中的研究 16D70 模、双模与理想（除16Gxx条款外）的结构与分类，以及结合代数中的直和分解与消去定理 16D80 关联代数中的其他类模块与理想[另见16G50] 16D90 联合代数中的模分类[另见16Gxx、16S90]；范畴论中的模理论；Morita等价与对偶性 16D99以上都不是，但本节如此 |
| 16Exx Homological methods in associative algebras {For commutative rings, see 13Dxx; for general categories, see 18Gxx} 16E05 Syzygies, resolutions, complexes in associative algebras 16E10 Homological dimension in associative algebras 16E20 Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50] 16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras 16E35 Derived categories and associative algebras 16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 16E45 Differential graded algebras and applications (associative algebraic aspects) 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. 16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 16E99 None of the above, but in this section |
16Exx 关联代数中的同源方法 {关于交换环，请参见 13Dxx；一般类别见18Gxx} 16E05关联代数中的合取、分解与复合 16E10关联代数中的同调维数 16E20 Grothendieck群、K理论等[另见18F30、19Axx、19D50] 16E30 关联代数中模的同源函子（Tor、Ext等） 16E35派生范畴和关联代数 16E40（共）同调理论中的环与结合代数（如霍希尔德代数、循环代数、二面体代数等） 16E45 微分分次代数及其应用（结合代数方面） 16E50 von Neumann正则环及其推广（结合代数方面） 16E60 半遗传环与遗传环、自由理想环、Sylvester环等。 16E65 关联环的同调条件（正则环、Gorenstein环、Cohen-Macaulay环等的推广） 16E99以上都不是，但属于本节 |
| 16Gxx Representation theory of associative rings and algebras 16G10 Representations of associative Artinian rings 16G20 Representations of quivers and partially ordered sets 16G30 Representations of orders, lattices, algebras over commutative rings [See also 16Hxx] 16G50 Cohen-Macaulay modules in associative algebras 16G60 Representation type (finite, tame, wild, etc.) of associative algebras 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 16G99 None of the above, but in this section |
16Gxx 交换环与代数的表示理论 16G10关联Artinian环的表示 16G20箭图和部分有序集的表示 16G30 交换环上的序、格、代数表示[另见16Hxx] 16G50 关联代数中的Cohen-Macaulay模 16G60 关联代数的表示类型（有限型、驯化型、野生型等） 16G70 Auslander-Reiten序列（近乎分裂序列）与Auslander-Reiten箭图 16G99以上都不是，但属于本节 |
| 16Hxx Associative algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30} 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16H10 Orders in separable algebras 16H15 Commutative orders 16H20 Lattices over orders 16H99 None of the above, but in this section |
16Hxx 关联代数与序论 {关于算术方面的内容，请参见11R52、11R54， 11S45；关于表示理论，参见16G30} 16H05 可分代数（例如四元数代数、Azumaya代数等） 16H10可分代数中的命令 16H15 交换顺序 16H20订单上的格子 16H99以上都不是，但本节如此 |
| 16Kxx Division rings and semisimple Artin rings [See also 12E15, 15A30] 16K20 Finite-dimensional division rings {For crossed products, see 16S35} 16K40 Infinite-dimensional and general division rings 16K50 Brauer groups (algebraic aspects) [See also 12G05, 14F22] 16K99 None of the above, but in this section |
16Kxx 分割环与半单Artin环[另见12E15、15A30] 16K20 有限维除环（关于交叉积的详细信息，请参见16S35） 16K40无限维与一般除环 16K50 Brauer群（代数方面）[另见12G05、14F22] 16K99以上都不是，但本节是 |
| 16Lxx Local rings and generalizations 16L30 Noncommutative local and semilocal rings, perfect rings 16L60 Quasi-Frobenius rings [See also 16D50] 16L99 None of the above, but in this section |
16Lxx 本地环与泛化 16L30 非交换局部与半局部环、完美环； 16L60 准弗罗贝尼乌斯环[另见16D50] 16L99以上都不是，但本节适用 |
| 16Nxx Radicals and radical properties of associative rings 16N20 Jacobson radical, quasimultiplication 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 16N60 Prime and semiprime associative rings [See also 16D60, 16U10] 16N80 General radicals and associative rings {For radicals in module categories, see 16S90} 16N99 None of the above, but in this section |
16Nxx 协同环的自由基及其性质 16N20 Jacobson 根式，准乘积 16N40 零与幂零根、集合、理想、结合环 16N60 Prime和半素数关联环[另见16D60、16U10] 16N80 一般自由基与关联环（模块范畴中的自由基参见16S90）； 16N99 以上均非，但本节 |
| 16Pxx Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 16P10 Finite rings and finite-dimensional associative algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} 16P20 Artinian rings and modules (associative rings and algebras) 16P40 Noetherian rings and modules (associative rings and algebras) 16P50 Localization and associative Noetherian rings [See also 16U20] 16P60 Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras) 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 16P90 Growth rate, Gelfand-Kirillov dimension 16P99 None of the above, but in this section |
16Pxx链条件、生长条件及其他形式的关联性有限性 环与代数 16P10 有限环与有限维结合代数（半单情形参见16K20；交换情形参见11Txx、13Mxx） 16P20 阿廷环与模（结合环与代数） 16P40 诺特环与模（结合环与代数） 16P50局域化与关联诺特环[另见16U20] 16P60 系统中湮灭子与和项的链条件：Goldie型条件[另见16U20]，以及Krull维数（适用于结合环与代数） 16P70链条件在其他类别的子模块、理想、子环等中的应用；同调性（结合环与代数） 16P90 生长率，Gelfand-Kirillov维度 16P99以上都不是，但本节如此 |
| 16Rxx Rings with polynomial identity 16R10 T-ideals, identities, varieties of associative rings and algebras 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16R30 Trace rings and invariant theory (associative rings and algebras) 16R40 Identities other than those of matrices over commutative rings 16R50 Other kinds of identities (generalized polynomial, rational, involution) 16R60 Functional identities (associative rings and algebras) 16R99 None of the above, but in this section |
16Rxx具有多项式恒等式的环 |
| 16Sxx Associative rings and algebras arising under various constructions 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16S20 Centralizing and normalizing extensions 16S30 Universal enveloping algebras of Lie algebras [See mainly 17B35] 16S32 Rings of differential operators (associative algebraic aspects) [See also 13N10, 32C38] 16S34 Group rings [See also 20C05, 20C07], Laurent polynomial rings (associative algebraic aspects) 16S35 Twisted and skew group rings, crossed products 16S36 Ordinary and skew polynomial rings and semigroup rings [See also 20M25] 16S37 Quadratic and Koszul algebras 16S38 Rings arising from noncommutative algebraic geometry [See also 14A22] 16S40 Smash products of general Hopf actions [See also 16T05] 16S50 Endomorphism rings; matrix rings [See also 15-XX] 16S60 Associative rings of functions, subdirect products, sheaves of rings 16S70 Extensions of associative rings by ideals 16S80 Deformations of associative rings [See also 13D10, 14D15] 16S85 Associative rings of fractions and localizations [See also 13B30] 16S88 Leavitt path algebras 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 16S99 None of the above, but in this section |
16Sxx在各种构造下产生的关联环和代数 16S10 由通用性质（自由代数、余积、逆元的附加等）确定的关联环 16S15 有限生成、有限可表示性、标准型（钻石引理、项重写） 16S20集中化和标准化扩展 16S30李代数的普遍包络代数[主要参见17B35] 16S32微分算子环（结合代数方面）[另见13N10,32C38] 16S34群环[另见20C05、20C07]，Laurent多项式环（结合代数特性） 16S35 扭曲与倾斜群环，交叉积 16S36 常规与斜多项式环及半群环[另见20M25] 16S37二次代数与Koszul代数 16S38非交换代数几何产生的环[另见14A22] 16S40通用Hopf动作的粉碎产品[另见16T05] 16S50内聚环；基质环[另见15-XX] 16S60 作用环、子直积、环层 16S70理想对关联环的扩展 16S80 联合环的变形[另见13D10、14D15] 16S85 分馏组分与定位的关联环 [另见13B30] 16S88Leavitt路径代数 16S90 扭转理论；模范畴上的根（结合代数方面）[另见13D30、18E40] {环的根，参见16Nxx} 16S99以上均不符合，但本节适用 |
| 16Txx Hopf algebras, quantum groups and related topics 16T05 Hopf algebras and their applications [See also 16S40, 57T05] 16T10 Bialgebras 16T15 Coalgebras and comodules; corings 16T20 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] 16T25 Yang-Baxter equations 16T30 Connections of Hopf algebras with combinatorics [See also 05Exx] 16T99 None of the above, but in this section |
16Txx Hopf代数、量子群及相关课题 16T05Hopf代数及其应用[另见16S40、57T05] 16T10 代数 16T15 余代数与余模；余核 16T20 量子群的环论方面[另见17B37、20G42、81R50] 16T25 Yang-Baxter方程 16T30 Hopf代数与组合学的联系[另见05Exx] 16T99以上都不是，但本节如此 |
| 16Uxx Conditions on elements 16U10 Integral domains (associative rings and algebras) 16U20 Ore rings, multiplicative sets, Ore localization 16U30 Divisibility, noncommutative UFDs 16U40 Idempotent elements (associative rings and algebras) 16U60 Units, groups of units (associative rings and algebras) 16U70 Center, normalizer (invariant elements) (associative rings and algebras) 16U80 Generalizations of commutativity (associative rings and algebras) 16U90 Generalized inverses (associative rings and algebras) 16U99 None of the above, but in this section |
16Uxx 元素条件 |
| 16Wxx Associative rings and algebras with additional structure 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 16W20 Automorphisms and endomorphisms 16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras) 16W25 Derivations, actions of Lie algebras 16W50 Graded rings and modules (associative rings and algebras) 16W55 “Super” (or “skew”) structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66} 16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) [See also 13Jxx] 16W70 Filtered associative rings; filtrational and graded techniques 16W80 Topological and ordered rings and modules [See also 06F25, 13Jxx] 16W99 None of the above, but in this section |
16Wxx附加结构的关联环与代数 16W10 退化环；Lie、Jordan及其他非结合结构[另见17B60、17C50、46Kxx] 16W20自同构与自同态 16W22 群与半群的运算；不变量理论（结合环与代数） 16W25导出与李代数的作用 16W50 等级环与模（结合环与代数） 16W55 “超”（或“斜”）结构[另见17A70、17Bxx、17C70] {外代数参见15A75；克利福德代数参见11E88、15A66} 16W60 估值、完成、正规幂级数及相关构造（结合环与代数）[另见13Jxx] 16W70过滤式关联环；过滤与分级技术 16W80拓扑有序环与模[另见06F25、13Jxx] 16W99以上都不是，但本节是 |
| 16Yxx Generalizations {For nonassociative rings, see 17-XX} 16Y20 Hyperrings 16Y30 Near-rings [See also 12K05] 16Y60 Semirings [See also 12K10] 16Y80 Γ and fuzzy structures 16Y99 None of the above, but in this section |
16Yxx推广（非结合环相关内容参见17-XX） 16Y20 超环 16Y30 近环[另见12K05] 16Y60半环[另见12K10] 16Y80 Γ 和模糊结构 16Y99以上都不是，但本节适用 |
| 16Zxx Computational aspects of associative rings {For software etc., see 16-04} 16Z05 Computational aspects of associative rings (general theory) [See also 68W30] 16Z10 Gr¨obner-Shirshov bases 16Z99 None of the above, but in this section |
16Zxx 联合环的计算方面 {软件等请参见16-04} 16Z05 关联环的计算方面（一般理论）[另见68W30] 16Z10格罗布纳-希尔绍夫基 16Z99以上都不是，但本节适用 |
| 17-XX Nonassociative rings and algebras 17-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras 17-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras 17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras 17-03 History of nonassociative rings and algebras [Consider also classification numbers from Section 01] 17-04 Software, source code, etc. for problems pertaining to nonassociative rings and algebras 17-06 Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras 17-08 Computational methods for problems pertaining to nonassociative rings and algebras [See also 68W30] 17-11 Research data for problems pertaining to nonassociative rings and algebras |
17-XX非结合环与代数 |
| 17Axx General nonassociative rings 17A01 General theory of nonassociative rings and algebras 17A05 Power-associative rings 17A15 Noncommutative Jordan algebras 17A20 Flexible algebras 17A30 Nonassociative algebras satisfying other identities 17A32 Leibniz algebras 17A35 Nonassociative division algebras 17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras) 17A40 Ternary compositions 17A42 Other n-ary compositions (n ≥ 3) 17A45 Quadratic algebras (but not quadratic Jordan algebras) 17A50 Free nonassociative algebras 17A60 Structure theory for nonassociative algebras 17A61 Gr¨obner-Shirshov bases in nonassociative algebras 17A65 Radical theory (nonassociative rings and algebras) 17A70 Superalgebras 17A75 Composition algebras 17A80 Valued algebras 17A99 None of the above, but in this section |
17Axx一般非关联环 17A01非结合环与代数的一般理论 17A05电力关联环 17A15非交换Jordan代数 17A20 灵活代数 17A30满足其他恒等式的非结合代数 17A32莱布尼茨代数 17A35非关联除法代数 17A36 自同构、导出、其他运算符（非结合环与代数） 17A40 三元组合 17A42其他n元组合（n≥3） 17A45 二次代数（但不包括二次Jordan代数） 17A50自由非结合代数 17A60非结合代数的结构理论 17A61 非结合代数中的Gröbner-Shirshov基 17A65 激发理论（非结合环与代数） 17A70 Superalgebras 17A75 代数结构 17A80 有值代数 17A99以上都不是，但属于本节 |
| 17Bxx Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} 17B01 Identities, free Lie (super)algebras 17B05 Structure theory for Lie algebras and superalgebras 17B08 Coadjoint orbits; nilpotent varieties 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B15 Representations of Lie algebras and Lie superalgebras, analytic theory 17B20 Simple, semisimple, reductive (super)algebras 17B22 Root systems 17B25 Exceptional (super)algebras 17B30 Solvable, nilpotent (super)algebras 17B35 Universal enveloping (super)algebras [See also 16S30] 17B37 Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 17B38 Yang-Baxter equations and Rota-Baxter operators 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17B45 Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 17B50 Modular Lie (super)algebras 17B55 Homological methods in Lie (super)algebras 17B56 Cohomology of Lie (super)algebras 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 17B61 Hom-Lie and related algebras 17B62 Lie bialgebras; Lie coalgebras 17B63 Poisson algebras 17B65 Infinite-dimensional Lie (super)algebras [See also 22E65] 17B66 Lie algebras of vector fields and related (super) algebras 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68 Virasoro and related algebras 17B69 Vertex operators; vertex operator algebras and related structures 17B70 Graded Lie (super)algebras 17B75 Color Lie (super)algebras 17B80 Applications of Lie algebras and superalgebras to integrable systems 17B81 Applications of Lie (super)algebras to physics, etc. 17B99 None of the above, but in this section |
17Bxx李代数与李超代数{关于李群，参见22Exx} 17B01身份，自由李（超）代数 17B05李代数与超代数的结构理论 17B08共轭轨道；幂零簇 17B10 李代数与李超代数的表示，代数理论（权重） 17B15 李代数与李超代数的表示，解析理论 17B20 简单、半简单、约化（超）代数 17B22 根系 17B25特殊（超）代数 17B30 可解的幂零（超）代数 17B35 通用包络（超）代数[另见16S30] 17B37 量子群（量子化包络代数）及相关变形[另见16T20、20G42、81R50、82B23] 17B38杨-巴克斯特方程和Rota-Baxter算子 17B40李代数与超代数的自同构、导出及其他运算符 17B45 线性代数群的李代数[另见14Lxx和20Gxx] 17B50 模李（超）代数 17B55李（超）代数中的同源方法 17B56李（超）代数同调 17B60 与其它结构（结合、Jordan等）相关的（超）代数[另见16W10、17C40、17C50] 17B61 Hom-Lie及相关代数 17B62李代数；李余代数 17B63泊松代数 17B65无限维李（超）代数[另见22E65] 17B66 矢量场的李代数及相关（超）代数 17B67 Kac-Moody（超）代数；扩展仿射李代数；环面李代数 17B68 Virasoro和相关代数 17B69顶点算子、顶点算子代数及相关结构 17B70 有界（超）代数 17B75颜色（超）代数 17B80李代数与超代数在可积系统中的应用 17B81李（超）代数在物理学等领域的应用。 17B99以上都不是，但属于本节 |
| 17Cxx Jordan algebras (algebras, triples and pairs) 17C05 Identities and free Jordan structures 17C10 Structure theory for Jordan algebras 17C17 Radicals in Jordan algebras 17C20 Simple, semisimple Jordan algebras 17C27 Idempotents, Peirce decompositions 17C30 Associated groups, automorphisms of Jordan algebras 17C36 Associated manifolds of Jordan algebras 17C37 Associated geometries of Jordan algebras 17C40 Exceptional Jordan structures 17C50 Jordan structures associated with other structures [See also 16W10] 17C55 Finite-dimensional structures of Jordan algebras 17C60 Division algebras and Jordan algebras 17C65 Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 17C70 Super structures 17C90 Applications of Jordan algebras to physics, etc. 17C99 None of the above, but in this section |
17Cxx Jordan代数（代数、三元组和配对） 17C05身份和自由约旦结构 17C10约旦代数的结构理论 17C17约旦代数中的根 17C20 简单半单Jordan代数 17C27幂等元，皮尔斯分解 17C30相关群，Jordan代数的自同构 17C36约旦代数的关联流形 17C37约旦代数的关联几何 17C40特殊型乔丹结构 17C50 Jordan结构与其他结构相关联[另见16W10] 17C55约旦代数的有限维结构 17C60 分割代数与约旦代数 17C65 约旦结构在巴拿赫空间和代数上的研究[另见46H70、46L70] 17C70 超结构 17C90约旦代数在物理学等领域的应用 17C99 以上均不适用，但本节另有规定 |
| 17Dxx Other nonassociative rings and algebras 17D05 Alternative rings 17D10 Mal’tsev rings and algebras 17D15 Right alternative rings 17D20 (γ, δ)-rings, including (1, −1)-rings 17D25 Lie-admissible algebras 17D30 (non-Lie) Hom algebras and topics 17D92 Genetic algebras 17D99 None of the above, but in this section |
17Dxx其他非结合环和代数 17D05 替代环 17D10马尔采夫环与代数 17D15 右侧备胎环 17D20（γ ，δ）环，包含（1，−1）环 17D25 可列代数 17D30（非李）同调代数与相关课题 17D92遗传代数 17D99以上都不是，但属于本节 |
| 18-XX Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 18-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory 18-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory 18-02 Research exposition (monographs, survey articles) pertaining to category theory 18-03 History of category theory [Consider also classification numbers from Section 01] 18-04 Software, source code, etc. for problems pertaining to category theory 18-06 Proceedings, conferences, collections, etc. pertaining to category theory 18-08 Computational methods for problems pertaining to category theory 18-11 Research data for problems pertaining to category theory |
18-XX范畴论；同调代数{交换环参见13Dxx；结合环参见16Exx；群参见20Jxx；拓扑群及相关结构参见57Txx；代数拓扑另见55Nxx、55Uxx} 18-00范畴论相关通用参考文献（手册、词典、书目等） 18-01范畴论入门性论述（教材、教程论文等） 18-02范畴论研究性论述（专著、综述文章等） 18-03范畴论发展史[另请参考第01节分类号] 18-04范畴论相关问题的软件、源代码等资源 18-06范畴论相关会议论文集、会议记录等文献 18-08范畴论相关计算方法 18-11范畴论相关研究数据 |
| 18Axx General theory of categories and functors 18A05 Definitions and generalizations in theory of categories 18A10 Graphs, diagram schemes, precategories 18A15 Foundations, relations to logic and deductive systems [See also 03-XX] 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A22 Special properties of functors (faithful, full, etc.) 18A23 Natural morphisms, dinatural morphisms 18A25 Functor categories, comma categories 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18A32 Factorization systems, substructures, quotient structures, congruences, amalgams 18A35 Categories admitting limits (complete categories), functors preserving limits, completions 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18A50 Graded categories (general) {For dg categories, see 18G35} 18A99 None of the above, but in this section |
18Axx范畴与函子的一般理论 18A05范畴论中的定义与推广 18A10图、图式与预范畴 18A15基础理论及其与逻辑及演绎系统的关联[另见03-XX] 18A20满射、单射、特殊类态射与零态射 18A22函子的特殊性质（忠实函子、满函子等） 18A23自然态射与双自然态射 18A25函子范畴与逗号范畴 18A30极限与余极限（乘积、和、有向极限、外推、纤维积、等化子、核、端与余端等） 18A32因子分解系统、子结构、商结构、同余、并合 18A35允许极限的范畴（完备范畴）、保持极限的函子、完备化 18A40伴随函子（普遍构造、反射子范畴、Kan扩张等） 18A50分级范畴（一般）{关于dg范畴，参见18G35} 18A99以上均不适用，但本节 |
| 18Bxx Special categories 18B05 Categories of sets, characterizations [See also 03-XX] 18B10 Categories of spans/cospans, relations, or partial maps 18B15 Embedding theorems, universal categories [See also 18E20] 18B20 Categories of machines, automata [See also 03D05, 68Qxx] 18B25 Topoi [See also 03G30, 18F10] 18B35 Preorders, orders, domains and lattices (viewed as categories) [See also 06-XX] 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 18B50 Extensive, distributive, and adhesive categories 18B99 None of the above, but in this section |
18Bxx 特殊范畴 18B05 集合的类别和特征[另见03-XX] 18B10 跨度/共跨度、关系或部分映射的分类 18B15嵌入定理，普遍范畴[另见18E20] 18B20 机器、自动机的分类[另见03D05、68Qxx] 18B25 Topoi[另见03G30、18F10] 18B35 预订、订单、域名和格子（视为类别）[另见06-XX] 18B40 群胚、半群胚、半群、群（视为范畴）[另见20Axx、20L05、20Mxx] 18B50 广泛、分配和粘性范畴 18B99以上都不是，但属于本节 |
| 18Cxx Categories and theories 18C05 Equational categories [See also 03C05, 08C05] 18C10 Theories (e.g., algebraic theories), structure, and semantics [See also 03G30] 18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads [See also 18Gxx] {For functional programming, see also 68N18} 18C20 Eilenberg-Moore and Kleisli constructions for monads 18C30 Sketches and generalizations 18C35 Accessible and locally presentable categories 18C40 Structured objects in a category (group objects, etc.) 18C50 Categorical semantics of formal languages [See also 68Q55, 68Q65] 18C99 None of the above, but in this section |
18Cxx范畴与理论 18C05等式范畴[另见03C05、08C05] 18C10理论（如代数理论）、结构与语义[另见03G30] 18C15单子（即标准构造、三元组或三元结构）、单子代数、单子同调与导出函子[另见18Gxx] {关于函数式编程，另见68N18} 18C20单子的艾伦伯格-摩尔构造与克莱斯利构造 18C30概要与推广 18C35可及范畴与局部可表范畴 18C40范畴中的结构化对象（群对象等） 18C50形式语言的范畴语义[另见68Q55、68Q65] 18C99不属于上述任何一项，但本节 |
| 18Dxx Categorical structures 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) 18D20 Enriched categories (over closed or monoidal categories) 18D25 Actions of a monoidal category, tensorial strength {For functional programming, see also 68N18} 18D30 Fibered categories 18D40 Internal categories and groupoids {For double categories, see 18N10; for topological groupoids, see 22A22; for Lie groupoids, see 58H05} 18D60 Profunctors (= correspondences, distributors, modules) 18D65 Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) 18D70 Formal category theory 18D99 None of the above, but in this section |
18Dxx范畴式结构 18D15 闭范畴（闭单形范畴、闭笛卡尔范畴等） 18D20富集类别（相较于闭合或单形类别） 18D25 单形范畴的运算与张量强度（函数式编程相关参见68N18） 18D30 光纤类别 18D40 内部范畴与群胚 {双范畴参见18N10；拓扑群胚参见22A22；李群胚参见58H05} 18D60 Profunctors（即对应、分配器、模块） 18D65 Proarrow设备，Yoneda结构， KZ 理论（松弛幂等单子） 18D70形式范畴论 18D99以上都不是，但本节是 |
| 18Exx Categorical algebra 18E05 Preadditive, additive categories 18E08 Regular categories, Barr-exact categories 18E10 Abelian categories, Grothendieck categories 18E13 Protomodular categories, semi-abelian categories, Mal’tsev categories [See also 08B05 and 18B10] 18E20 Categorical embedding theorems [See also 18B15] 18E35 Localization of categories, calculus of fractions {For homotopical aspects, see also 18N55, 55P60} 18E40 Torsion theories, radicals [See also 13D30, 16S90] 18E45 Definable subcategories and connections with model theory [See also 13C60] 18E50 Categorical Galois theory 18E99 None of the above, but in this section |
18Exx 离散代数 18E05 预加法范畴与加法范畴 18E08 正则范畴与巴尔正合范畴 18E10 阿贝尔范畴与格罗滕迪克范畴 18E13 原模范畴、半阿贝尔范畴与马尔采夫范畴[另见08B05和18B10] 18E20 离散嵌入定理[另见18B15] 18E35 范畴局部化与分数演算{关于同伦方面，另见18N55、55P60} 18E40 扭理论与根[另见13D30、16S90] 18E45 可定义子范畴及其与模型论的联系[另见13C60] 18E50 离散伽罗瓦理论 18E99 以上均不包含，但本节 |
| 18Fxx Categories in geometry and topology 18F05 Local categories and functors 18F10 Grothendieck topologies and Grothendieck topoi [See also 14F20, 18B25] 18F15 Abstract manifolds and fiber bundles (category-theoretic aspects) [See also 55Rxx, 57Pxx] 18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) [See also 14F06, 14F08, 32C35, 32L10, 54B40, 55N30] 18F25 Algebraic K-theory and L-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 18F30 Grothendieck groups (category-theoretic aspects) [See also 13D15, 16E20, 19Axx] 18F40 Synthetic differential geometry, tangent categories, differential categories 18F50 Goodwillie calculus and functor calculus 18F60 Categories of topological spaces and continuous mappings [See also 54-XX] 18F70 Frames and locales, pointfree topology, Stone duality [See also 06D22, 18B35] 18F75 Quantales [See also 06F07, 18B35] 18F99 None of the above, but in this section |
18Fxx 几何与拓扑学中的范畴 18F05本地范畴和函子 18F10 Grothendieck拓扑与Grothendieck拓扑空间[另见14F20、18B25] 18F15 抽象流形与纤维丛（范畴论方面）[另见55Rxx、57Pxx] 18F20预切片与切片、堆叠、下降条件（范畴论方面）[另见14F06、14F08、32C35、32L10、54B40、55N30] 18F25 代数K理论与L理论（范畴论方面）[另见11Exx、11R70、11S70、12-XX、13D15、14Cxx、16E20、19-XX、46L80、57R65、57R67] 18F30 Grothendieck群（范畴论方面）[另见13D15、16E20、19Axx] 18F40 合成微分几何、切线范畴、微分范畴 18F50Goodwillie微积分与函子微积分 18F60拓扑空间与连续映射的分类[另见54-XX] 18F70框架与局部，无点拓扑，Stone对偶[另见06D22,18B35] 18F75 Quantales[另见06F07、18B35] 18F99以上均不符合，但本节适用 |
| 18Gxx Homological algebra in category theory, derived categories and functors [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx] 18G05 Projectives and injectives (category-theoretic aspects) [See also 13C10, 13C11, 16D40, 16D50] 18G10 Resolutions; derived functors (category-theoretic aspects) [See also 13D02, 16E05, 18Gxx] 18G15 Ext and Tor, generalizations, K¨unneth formula (category-theoretic aspects) [See also 55U25] 18G20 Homological dimension (category-theoretic aspects) [See also 13D05, 16E10] 18G25 Relative homological algebra, projective classes (category-theoretic aspects) 18G31 Simplicial modules and Dold-Kan correspondence 18G35 Chain complexes (category-theoretic aspects), dg categories [See also 14F08, 18G80, 55U15] 18G40 Spectral sequences, hypercohomology [See also 55Txx] 18G45 2-groups, crossed modules, crossed complexes 18G50 Nonabelian homological algebra (category-theoretic aspects) 18G65 Stable module categories [See also 20C20] 18G70 A∞-categories, relations with homological mirror symmetry [See also 14F08, 14J33, 53D37] 18G80 Derived categories, triangulated categories 18G85 Graph complexes and graph homology {For relations with deformation quantization, see 53D55} 18G90 Other (co)homology theories (category-theoretic aspects) [See also 19D55, 46L80, 58J20, 58J22] 18G99 None of the above, but in this section |
18Gxx范畴论中的同源代数、导出范畴与函子[另见13Dxx、16Exx、20Jxx、55Nxx、55Uxx、57Txx] 18G05投射映射和满射（范畴论方面）[另见13C10、13C11、16D40、16D50] 18G10解析；导出函子（范畴论方面）[另见13D02、16E05、18Gxx] 18G15 Ext和Tor，推广，Kunneth公式（范畴论方面）[另见55U25] 18G20同调维数（范畴论方面）[另见13D05、16E10] 18G25 相对同调代数，射影类（范畴论方面） 18G31单纯模与Dold-Kan对应 18G35 链复形（范畴论方面），dg范畴[另见14F08、18G80、55U15]； 18G40 谱序列，超同调[另见55Txx] 18G45 2-组，交叉模块，交叉复合体 18G50 非阿贝尔同调代数（范畴论方面） 18G65稳定模块类别[另请参见20C20] 18G70 A∞-范畴，与同调镜像对称的关系[另见14F08、14J33、53D37] 18G80 派生类别，三角化类别 18G85 图复合体与图同调（与形变量子化相关的内容参见53D55）； 18G90 其他（上）同调理论（范畴论视角）[另见19D55、46L80、58J20、58J22] 18G99以上都不是，但本节适用 |
| 18Mxx Monoidal categories and operads 18M05 Monoidal categories, symmetric monoidal categories [See also 19D23] 18M10 Traced monoidal categories, compact closed categories, star-autonomous categories 18M15 Braided monoidal categories and ribbon categories {For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50} 18M20 Fusion categories, modular tensor categories, modular functors {For applications to topological quantum field theories, see also 57R56; for applications to conformal field theories, see also 81T40} 18M25 Tannakian categories {For applications to motives, see also 14C15, 19E15} 18M30 String diagrams and graphical calculi 18M35 Categories of networks and processes, compositionality 18M40 Dagger categories, categorical quantum mechanics [See also 81P68] 18M45 Categorical aspects of linear logic [See also 03B47] 18M50 Bimonoidal, skew-monoidal, duoidal categories 18M60 Operads (general) 18M65 Non-symmetric operads, multicategories, generalized multicategories 18M70 Algebraic operads, cooperads, and Koszul duality 18M75 Topological and simplicial operads [See also 18N60] 18M80 Species, Hopf monoids, operads in combinatorics 18M85 Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads 18M90 Globular operads 18M99 None of the above, but in this section |
18Mxx 单子范畴与运算子 18M05 单子范畴，对称单子范畴[另见19D23] 18M10 追踪单子范畴，紧闭范畴，星自洽范畴 18M15 编辫单子范畴与带状范畴{在纽结理论中的应用另见57Kxx；在量子群中的应用另见16T20、17B37、81R50} 18M20 融合范畴，模张量范畴，模函子{在拓扑量子场论中的应用另见57R56；在共形场论中的应用另见81T40} 18M25 坦纳基范畴{在动机理论中的应用另见14C15、19E15} 18M30 弦图与图形演算 18M35 网络与过程范畴，组合性 18M40 锋范畴，范畴量子力学[另见81P68] 18M45 线性逻辑的范畴化研究[另见03B47] 18M50 双单子范畴，斜单子范畴，双对偶范畴 18M60 运算子（广义） 18M65 非对称运算子，多重范畴，广义多重范畴 18M70 代数运算子，合作运算子，科祖尔对偶性 18M75 拓扑与单纯运算子[另见18N60] 18M80 物种，霍普夫幺半群，组合学中的运算子 18M85 多重范畴/双运算子，真运算子，PROPs，循环运算子，模运算子 18M90 球面运算子 18M99 上述均不适用，但本节 |
| 18Nxx Higher categories and homotopical algebra 18N10 2-categories, bicategories, double categories 18N15 2-dimensional monad theory [See also 18C15] 18N20 Tricategories, weak n-categories, coherence, semi-strictification 18N25 Categorification 18N30 Strict omega-categories, computads, polygraphs 18N40 Homotopical algebra, Quillen model categories, derivators [See also 55U35] 18N45 Categories of fibrations, relations to K-theory, relations to type theory 18N50 Simplicial sets, simplicial objects [See also 55U10] 18N55 Localizations (e.g., simplicial localization, Bousfield localization) [See also 18E35, 55P60] 18N60 (∞, 1)-categories (quasi-categories, Segal spaces, etc.); ∞-topoi, stable ∞-categories [See also 55U35, 55U40] 18N65 (∞, n)-categories and (∞, ∞)-categories 18N70 ∞-operads and higher algebra [See also 18M75] 18N99 None of the above, but in this section |
18Nxx 高阶范畴与同伦代数 18N10 2-范畴、双范畴、双层范畴 18N15 二维单子理论[另见18C15] 18N20 三范畴、弱n-范畴、凝聚性、半严格化 18N25 范畴化 18N30 严格ω-范畴、计算对象、多图 18N40 同伦代数、奎伦模范畴、导出子[另见55U35] 18N45 纤维化范畴、与K理论的关系、与类型论的关系 18N50 简单集、简单对象[另见55U10] 18N55 局部化（如简单集局部化、布斯菲尔德局部化）[另见18E35、55P60] 18N60（∞，1）-范畴（拟范畴、塞格尔空间等）；∞-拓扑、稳定∞-范畴[另见55U35、55U40] 18N65（∞，n）-范畴与（∞，∞）-范畴 18N70 ∞-运算子与高阶代数[另见18M75] 18N99 上述均不涉及，但本节 |
| 19-XX K-theory [See also 16E20, 18F25] 19-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to K-theory 19-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to K-theory 19-02 Research exposition (monographs, survey articles) pertaining to K-theory 19-03 History of K-theory [Consider also classification numbers from Section 01] 19-04 Software, source code, etc. for problems pertaining to K-theory 19-06 Proceedings, conferences, collections, etc. pertaining to K-theory 19-08 Computational methods for problems pertaining to K-theory 19-11 Research data for problems pertaining to K-theory |
19-XX K理论[另见16E20、18F25] 19-00 与K理论相关的通用参考文献（手册、词典、参考书目等）； 19-01 与K理论相关的入门性论述（教科书、教程论文等） 19-02 K理论研究进展综述（专著、综述） 19-03 K理论的历史[另请参阅第01节的分类编号] 19-04 K理论相关问题的软件、源代码等 19-06 与K理论相关的会议记录、会议、文集等 19-08 K理论相关问题的计算方法 19-11 K理论相关问题的研究数据 |
| 19Axx Grothendieck groups and K0 [See also 13D15, 18F30] 19A13 Stability for projective modules [See also 13C10] 19A15 Efficient generation of modules 19A22 Frobenius induction, Burnside and representation rings 19A31 K0 of group rings and orders 19A49 K0 of other rings 19A99 None of the above, but in this section |
19Axx Grothendieck群和K0[另见13D15、18F30] 19A13射影模的稳定性[另见13C10] 19A15模块高效生成 19A22 Frobenius归纳法、Burnside定理与表示环 19A31 K0的群环与阶 19A49 K0的其他环 19A99以上均不符合，但本节适用 |
| 19Bxx Whitehead groups and K1 19B10 Stable range conditions 19B14 Stability for linear groups 19B28 K1 of group rings and orders [See also 57Q10] 19B37 Congruence subgroup problems [See also 20H05] 19B99 None of the above, but in this section |
19Bxx Whitehead组和K1 19B10 稳定范围条件 19B14线性基团的稳定性 19B28 K1的群环和群阶[另见57Q10] 19B37 一致性子组问题[另见20H05] 19B99 以上均不适用，但本节 |
| 19Cxx Steinberg groups and K2 19C09 Central extensions and Schur multipliers 19C20 Symbols, presentations and stability of K2 19C30 K2 and the Brauer group 19C40 Excision for K2 19C99 None of the above, but in this section |
19Cxx Steinberg组和K2 19C09中心扩张与Schur乘子 19C20 K2的符号、表示方法和稳定性 19C30 K2和Brauer群 19C40 K2切除术 19C99以上都不是，但本节是 |
| 19Dxx Higher algebraic K-theory 19D06 Q- and plus-constructions 19D10 Algebraic K-theory of spaces 19D23 Symmetric monoidal categories [See also 18M05] 19D25 Karoubi-Villamayor-Gersten K-theory 19D35 Negative K-theory, NK and Nil 19D45 Higher symbols, Milnor K-theory 19D50 Computations of higher K-theory of rings [See also 13D15, 16E20] 19D55 K-theory and homology; cyclic homology and cohomology [See also 18G90] 19D99 None of the above, but in this section |
19Dxx高等代数K理论 19D06 Q型及Plus型结构 19D10空间的代数K理论 19D23对称单形范畴[另见18M05] 19D25 卡鲁比-维拉马约尔-格斯坦 K-理论 19D35负K理论， NK 和Nil 19D45 高级符号，Milnor K理论 19D50 环的高阶K理论计算 [另见 13D15,16E20] 19D55 K理论与同调；循环同调与上同调[另见18G90]； 19D99 以上均非，但本节 |
| 19Exx K-theory in geometry 19E08 K-theory of schemes [See also 14C35] 19E15 Algebraic cycles and motivic cohomology (K-theoretic aspects) [See also 14C25, 14C35, 14F42] 19E20 Relations of K-theory with cohomology theories [See also 14Fxx] 19E99 None of the above, but in this section |
19Exx 几何中的K理论 9E08 策略的K理论[另见14C35] 19E15 代数循环与动机上同调（K理论方面）[另见14C25、14C35、14F42]； 19E20 K理论与上同调理论的关系[另见14Fxx] 19E99以上都不是，但本节如此 |
| 19Fxx K-theory in number theory [See also 11R70, 11S70] 19F05 Generalized class field theory (K-theoretic aspects) [See also 11G45] 19F15 Symbols and arithmetic (K-theoretic aspects) [See also 11R37] 19F27 Etale cohomology, higher regulators, zeta and ´ L-functions (K-theoretic aspects) [See also 11G40, 11R42, 11S40, 14F20, 14G10] 19F99 None of the above, but in this section |
19Fxx 数论中的K理论[另见11R70、11S70] 19F05广义类域论（K理论方面）[另见11G45] 19F15 符号与算术（K理论方面）[另见11R37] 19F27 展开上同调、高阶调节器、ζ函数与L函数（K理论方面）[另见11G40、11R42、11S40、14F20、14G10] 19F99以上都不是，但本节如此 |
| 19Gxx K-theory of forms [See also 11Exx] 19G05 Stability for quadratic modules 19G12 Witt groups of rings [See also 11E81] 19G24 L-theory of group rings [See also 11E81] 19G38 Hermitian K-theory, relations with K-theory of rings 19G99 None of the above, but in this section |
19Gxx 形式的K理论[另见11Exx] 19G05二次模块稳定性 19G12 环的Witt群[另见11E81] 19G24 群环的L理论[另见11E81] 19G38 赫尔米特K理论，与环K理论的关系； 19G99 上述均不适用，但本节 |
| 19Jxx Obstructions from topology 19J05 Finiteness and other obstructions in K0 19J10 Whitehead (and related) torsion 19J25 Surgery obstructions (K-theoretic aspects) [See also 57R67] 19J35 Obstructions to group actions (K-theoretic aspects) 19J99 None of the above, but in this section |
19Jxx 拓扑学障碍 19J05 有限性及其他K0中的障碍 19J10 怀特海（及相关）挠率 19J25 手术障碍（K理论方面）[另见57R67] 19J35 群作用障碍（K理论方面） 19J99 以上均非，但本节 |
| 19Kxx K-theory and operator algebras [See mainly 46L80, and also 46M20] 19K14 K0 as an ordered group, traces |
19Kxx K理论与算子代数[主要参见46L80，另见46M20] 19K14 K0作为有序群的迹 |
| 19K33 Ext and K-homology [See also 55N22] 19K35 Kasparov theory (KK-theory) [See also 58J22] 19K56 Index theory [See also 58J20, 58J22] 19K99 None of the above, but in this section |
19K33延伸区与K同源性[另见55N22]
19K35 卡斯帕罗夫理论（KK理论）[另见58J22] |
| 19Lxx Topological K-theory [See also 55N15, 55R50, 55S25] 19L10 Riemann-Roch theorems, Chern characters 19L20 J-homomorphism, Adams operations [See also 55Q50] 19L41 Connective K-theory, cobordism [See also 55N22] 19L47 Equivariant K-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] 19L50 Twisted K-theory; differential K-theory 19L64 Geometric applications of topological K-theory 19L99 None of the above, but in this section |
19Lxx 拓扑K理论 [另见55N15、55R50、55S25] 19L10 黎曼-罗克定理与陈特征 19L20 J-同态与亚当斯操作 [另见55Q50] 19L41 连接K理论与配边 [另见55N22] 19L47 等变K理论 [另见55N91、55P91、55Q91、55R91、55S91] 19L50 扭曲K理论与微分K理论 19L64 拓扑K理论的几何应用 19L99 以上均非，但本节 |
| 19Mxx Miscellaneous applications of K-theory 19M05 Miscellaneous applications of K-theory 19M99 None of the above, but in this section |
19Mxx K理论的其他应用 19M05 K理论的其他应用 19M99 以上均非，但本节 |
| 20-XX Group theory and generalizations 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory 20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory 20-02 Research exposition (monographs, survey articles) pertaining to group theory 20-03 History of group theory [Consider also classification numbers from Section 01] 20-04 Software, source code, etc. for problems pertaining to group theory 20-06 Proceedings, conferences, collections, etc. pertaining to group theory 20-08 Computational methods for problems pertaining to group theory 20-11 Research data for problems pertaining to group theory |
20-XX 群论与推广 20-00 群论相关通用参考文献（手册、词典、参考书目等） 20-01 群论入门读物（教材、教程论文等） 20-02 群论研究专著（专著、综述文章） 20-03 群论发展史 [另请参考第01节分类号] 20-04 群论问题相关软件、源代码等 20-06 会议论文集、会议记录、与群论相关的文献汇编等 20-08 群论问题的计算方法 20-11 群论问题的研究数据 |
| 20Axx Foundations 20A05 Axiomatics and elementary properties of groups 20A10 Metamathematical considerations in group theory {For word problems, see 20F10} 20A15 Applications of logic to group theory 20A99 None of the above, but in this section |
20Axx 基础
20A05 群的公理化与基本性质 |
| 20Bxx Permutation groups 20B05 General theory for finite permutation groups 20B07 General theory for infinite permutation groups 20B10 Characterization theorems for permutation groups 20B15 Primitive groups 20B20 Multiply transitive finite groups 20B22 Multiply transitive infinite groups 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 20B27 Infinite automorphism groups [See also 12F10] 20B30 Symmetric groups 20B35 Subgroups of symmetric groups 20B99 None of the above, but in this section |
20Bxx 置换群 20B05 有限置换群的一般理论 20B07 无限置换群的一般理论 20B10 置换群的特征定理 20B15 原始群 20B20 乘法传递有限群 20B22 乘法传递无限群 20B25 代数、几何或组合结构的有限自同构群 [另见 05Bxx、12F10、20G40、20H30、51-XX] 20B27 无限自同构群 [另见 12F10] 20B30 对称群 20B35 对称群的子群 20B99 以上均非，但本节 |
| 20Cxx Representation theory of groups {For representation rings and Burnside rings, see also 19A22} 20C05 Group rings of finite groups and their modules (group-theoretic aspects) [See also 16S34] 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) [See also 16S34] 20C08 Hecke algebras and their representations 20C10 Integral representations of finite groups 20C11 p-adic representations of finite groups 20C12 Integral representations of infinite groups 20C15 Ordinary representations and characters 20C20 Modular representations and characters 20C25 Projective representations and multipliers 20C30 Representations of finite symmetric groups 20C32 Representations of infinite symmetric groups 20C33 Representations of finite groups of Lie type 20C34 Representations of sporadic groups 20C35 Applications of group representations to physics and other areas of science 20C99 None of the above, but in this section |
20Cxx 群的表示理论 {针对表示环与伯恩赛德环，另见19A22} 20C05 有限群的群环及其模（群论方面）[另见16S34] 20C07 无限群的群环及其模（群论方面）[另见16S34] 20C08 赫克代数及其表示 20C10 有限群的积分表示 20C11 有限群的p进表示 20C12 无限群的积分表示 20C15 普通表示与特征 20C20 模表示与特征 20C25 投影表示与乘子 20C30 有限对称群的表示 20C32 无限对称群的表示 20C33 有限李型群的表示 20C34 斑点群的表示 20C35 群表示在物理学及其他科学领域的应用 20C99 以上均非，但本节 |
| 20Dxx Abstract finite groups 20D05 Finite simple groups and their classification 20D06 Simple groups: alternating groups and groups of Lie type [See also 20Gxx] 20D08 Simple groups: sporadic groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks [See also 20F17] 20D15 Finite nilpotent groups, p-groups 20D20 Sylow subgroups, Sylow properties, π-groups, π-structure 20D25 Special subgroups (Frattini, Fitting, etc.) 20D30 Series and lattices of subgroups 20D35 Subnormal subgroups of abstract finite groups 20D40 Products of subgroups of abstract finite groups 20D45 Automorphisms of abstract finite groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D99 None of the above, but in this section |
20Dxx 摘要 有限群 20D05 有限单群及其分类 20D06 单群：交错群与李型群[另见20Gxx] 20D08 单群：零星群 20D10 有限可解群、群形理论、舒恩克类、菲廷类、π-长度、秩[另见20F17] 20D15 有限幂零群、p-群 20D20 西洛子群、西洛性质、π-群、π-结构 20D25 特殊子群（弗拉蒂尼、菲廷）等） 20D30 系列及子群格 20D35 抽象有限群的次正规子群 20D40 抽象有限群子群的积 20D45 抽象有限群的自同构 20D60 涉及抽象有限群的算术与组合问题 20D99 以上均非，但本节 |
| 20Exx Structure and classification of infinite or finite groups 20E05 Free nonabelian groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E07 Subgroup theorems; subgroup growth 20E08 Groups acting on trees [See also 20F65] 20E10 Quasivarieties and varieties of groups 20E15 Chains and lattices of subgroups, subnormal subgroups [See also 20F22] 20E18 Limits, profinite groups 20E22 Extensions, wreath products, and other compositions of groups [See also 20J05] 20E25 Local properties of groups 20E26 Residual properties and generalizations; residually finite groups 20E28 Maximal subgroups 20E32 Simple groups [See also 20D05] 20E34 General structure theorems for groups 20E36 Automorphisms of infinite groups {For automorphisms of finite groups, see 20D45} 20E42 Groups with a BN-pair; buildings [See also 51E24] 20E45 Conjugacy classes for groups 20E99 None of the above, but in this section |
20Exx 无限群与有限群的结构与分类 20E05 自由非阿贝尔群 20E06 群的自由积、自由积与并合、Higman-Neumann-Neumann扩张及其推广 20E07 子群定理；子群增长 20E08 作用于树的群 [另见 20F65] 20E10 群的拟簇与簇 20E15 子群链与格、次正规子群 [另见 20F22] 20E18 极限与有限群 20E22 扩张、花环积及其他群的组合 [另见 20J05] 20E25 群的局部性质 20E26 残余性质与推广；剩余有限群 20E28 最大子群 20E32 简单群[另见20D05] 20E34 群的一般结构定理 20E36 无限群的自同构{关于有限群的自同构，参见20D45} 20E42 具有BN对的群；建筑[另见51E24] 20E45 群的共轭类 20E99 以上均非，但本节 |
| 20Fxx Special aspects of infinite or finite groups 20F05 Generators, relations, and presentations of groups 20F06 Cancellation theory of groups; application of van Kampen diagrams [See also 57M05] 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20F11 Groups of finite Morley rank [See also 03C45, 03C60] 20F12 Commutator calculus 20F14 Derived series, central series, and generalizations for groups 20F16 Solvable groups, supersolvable groups [See also 20D10] 20F17 Formations of groups, Fitting classes [See also 20D10] 20F18 Nilpotent groups [See also 20D15] 20F19 Generalizations of solvable and nilpotent groups 20F22 Other classes of groups defined by subgroup chains 20F24 FC-groups and their generalizations 20F28 Automorphism groups of groups [See also 20E36] 20F29 Representations of groups as automorphism groups of algebraic systems 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) [See also 57M05, 57Sxx] 20F36 Braid groups; Artin groups 20F38 Other groups related to topology or analysis 20F40 Associated Lie structures for groups 20F45 Engel conditions 20F50 Periodic groups; locally finite groups 20F55 Reflection and Coxeter groups (group-theoretic aspects) [See also 22E40, 51F15] 20F60 Ordered groups (group-theoretic aspects) [See mainly 06F15] 20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67 Hyperbolic groups and nonpositively curved groups 20F69 Asymptotic properties of groups 20F70 Algebraic geometry over groups; equations over groups 20F99 None of the above, but in this section |
20Fxx 无限群或有限群的特殊方面
20F05 发生器、关系及组的表示 |
| 20Gxx Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55} 20G05 Representation theory for linear algebraic groups 20G07 Structure theory for linear algebraic groups 20G10 Cohomology theory for linear algebraic groups 20G15 Linear algebraic groups over arbitrary fields 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 20G25 Linear algebraic groups over local fields and their integers 20G30 Linear algebraic groups over global fields and their integers 20G35 Linear algebraic groups over ad`eles and other rings and schemes 20G40 Linear algebraic groups over finite fields 20G41 Exceptional groups 20G42 Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50] 20G43 Schur and q-Schur algebras 20G44 Kac-Moody groups 20G45 Applications of linear algebraic groups to the sciences 20G99 None of the above, but in this section |
20Gxx 线性代数群及相关主题 {算术理论参见11E57、11H56；几何理论参见14Lxx、22Exx；关于表示论的其他方法，可参阅以下文献：15A30、22E45、22E46、22E47、22E50、22E55； 20G05《线性代数群的表示论》； 20G07《线性代数群的结构论》； 20G10《线性代数群的上同调论》； 20G15《任意域上的线性代数群》； 20G20《实数域与复数域上的线性代数群》。四元数 20G25 局域域上的线性代数群及其整数 20G30 全域上的线性代数群及其整数 20G35 阿德莱尔及其他环与概形上的线性代数群 20G40 有限域上的线性代数群 20G41 异常群 20G42 量子群（量子化函数代数）及其表示 [另见 16T20,17B37，81R50] 20G43 Schur与q-Schur代数 20G44 Kac-Moody群 20G45 线性代数群在科学中的应用 20G99 以上均非，但本节 |
| 20Hxx Other groups of matrices [See also 15A30] 20H05 Unimodular groups, congruence subgroups (group-theoretic aspects) [See also 11F06, 19B37, 22E40, 51F20] 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) [See also 11F06, 22E40, 30F35, 32Nxx] 20H15 Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25] 20H20 Other matrix groups over fields 20H25 Other matrix groups over rings 20H30 Other matrix groups over finite fields 20H99 None of the above, but in this section |
20Hxx 其他矩阵群[另见15A30] 20H05 单模群与同余子群（群论方面）[另见11F06、19B37、22E40、51F20] 20H10 富克斯群及其推广（群论方面）[另见11F06、22E40、30F35、32Nxx] 20H15 其他几何群（含晶体学群）[另见51-XX，特别是51F15]以及82D25] 20H20 环上的其他矩阵群 20H25 环上的其他矩阵群 20H30 有限域上的其他矩阵群 20H99 以上均非，但本节 |
| 20Jxx Connections of group theory with homological algebra and category theory 20J05 Homological methods in group theory 20J06 Cohomology of groups 20J15 Category of groups 20J99 None of the above, but in this section |
20Jxx 群论与同调代数及范畴论的联系 20J05 群论中的同调方法 20J06 群的上同调 20J15 群的范畴 20J99 以上均非，但本节 |
| 20Kxx Abelian groups 20K01 Finite abelian groups {For sumsets, see 11B13, 11P70} 20K10 Torsion groups, primary groups and generalized primary groups 20K15 Torsion-free groups, finite rank 20K20 Torsion-free groups, infinite rank 20K21 Mixed groups 20K25 Direct sums, direct products, etc. for abelian groups 20K27 Subgroups of abelian groups 20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups 20K35 Extensions of abelian groups 20K40 Homological and categorical methods for abelian groups 20K45 Topological methods for abelian groups [See also 22A05, 22B05] 20K99 None of the above, but in this section |
20Kxx阿贝尔群
20K01 有限阿贝尔群 {关于和集，参见11B13、11P70} |
| 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05} 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05} 20L99 None of the above, but in this section |
20Lxx 群胚（即所有态射均为同构的小范畴）{关于具有单一二元运算的集合，参见20N02；关于拓扑群胚，参见22A22、58H05} 20L05 群胚（即所有态射均为同构的小范畴）{关于具有单一二元运算的集合，参见20N02；关于拓扑群胚，参见22A22、58H05} 20L99 以上均不适用，但本节 |
| 20Mxx Semigroups 20M05 Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10] 20M07 Varieties and pseudovarieties of semigroups 20M10 General structure theory for semigroups 20M11 Radical theory for semigroups 20M12 Ideal theory for semigroups 20M13 Arithmetic theory of semigroups 20M14 Commutative semigroups 20M15 Mappings of semigroups 20M17 Regular semigroups 20M18 Inverse semigroups 20M19 Orthodox semigroups 20M20 Semigroups of transformations, relations, partitions, etc. [See also 47D03, 47H20, 54H15] 20M25 Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60] 20M30 Representation of semigroups; actions of semigroups on sets 20M32 Algebraic monoids 20M35 Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50] 20M50 Connections of semigroups with homological algebra and category theory 20M75 Generalizations of semigroups 20M99 None of the above, but in this section |
20Mxx 半群 20M05 自由半群、生成元与关系、文字问题[另见03D40、08A50、20F10] 20M07 半群的簇与伪簇 20M10 半群的广义结构理论 20M11 半群的根理论 20M12 半群的理想理论 20M13 半群的算术理论 20M14 交换半群 20M15 半群的映射 20M17 正则半群 20M18 逆半群 20M19 正交半群 20M20 变换、关系、划分的半群等。[另见47D03、47H20、54H15] 20M25 半群环与环的乘法半群[另见16S36、16Y60] 20M30 半群表示法；半群在集合上的作用 20M32 代数幺半群 20M35 自动机理论、语言学等领域的半群应用[另见03D05、68Q70、68T50] 20M50 半群与同调代数及范畴论的关联 20M75 半群的推广形式 20M99 以上均非，但本节 |
| 20Nxx Other generalizations of groups 20N02 Sets with a single binary operation (groupoids) {For groupoids in connection with category theory, see 20L05; for topological groupoids, see 22A22, 58H05} 20N05 Loops, quasigroups [See also 05Bxx] 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.) 20N15 n-ary systems (n ≥ 3) 20N20 Hypergroups 20N25 Fuzzy groups [See also 03E72] 20N99 None of the above, but in this section 20Pxx Probabilistic methods in group theory [See also 60Bxx] 20P05 Probabilistic methods in group theory [See also 60Bxx] 20P99 None of the above, but in this section |
20Nxx 群的其他推广形式 20N02 具有单一二元运算的集合（群胚）{关于范畴论中的群胚，参见20L05；关于拓扑群胚的详细内容，请参阅22A22、58H05} 20N05《环路与拟群》[另见05Bxx] 20N10《三元系统（堆、半堆、堆胚等）》 20N15《n元系统（n≥3）》 20N20《超群》 20N25《模糊群》[另见03E72] 20N99《以上均非，但本节内容》 20Pxx《群论中的概率方法》[另见60Bxx] 20P05《群论中的概率方法》[另见60Bxx] 20P99《以上均非，但本节内容》 |
| 22Axx Topological and differentiable algebraic systems {For topological rings and fields, see 12Jxx, 13Jxx, 16W80} 22A05 Structure of general topological groups 22A10 Analysis on general topological groups 22A15 Structure of topological semigroups 22A20 Analysis on topological semigroups 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 22A25 Representations of general topological groups and semigroups 22A26 Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30] 22A30 Other topological algebraic systems and their representations 22A99 None of the above, but in this section |
22Axx 拓扑与可微分代数系统 {关于拓扑环与域的讨论，参见12Jxx、13Jxx、16W80} 22A05 一般拓扑群的结构 |
| 22Bxx Locally compact abelian groups (LCA groups) 22B05 General properties and structure of LCA groups 22B10 Structure of group algebras of LCA groups 22B99 None of the above, but in this section |
22Bxx 局部紧致阿贝尔群（LCA群） 22B05 LCA（生命周期评估）组的通用属性与结构 |
| 22Cxx Compact groups 22C05 Compact groups 22C99 None of the above, but in this section |
22Cxx 紧凑型群组 22C05 紧凑型群组 |
| 22Dxx Locally compact groups and their algebras 22D05 General properties and structure of locally compact groups 22D10 Unitary representations of locally compact groups 22D12 Other representations of locally compact groups 22D15 Group algebras of locally compact groups 22D20 Representations of group algebras 22D25 C ∗ -algebras and W∗ -algebras in relation to group representations [See also 46Lxx] 22D30 Induced representations for locally compact groups 22D35 Duality theorems for locally compact groups 22D40 Ergodic theory on groups [See also 28Dxx] 22D45 Automorphism groups of locally compact groups 22D50 Rigidity in locally compact groups 22D55 Kazhdan’s property (T), the Haagerup property, and generalizations 22D99 None of the above, but in this section |
22Dxx局部紧群及其代数 22D05 局部紧致群的一般性质与结构 |
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