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**►****Foundations****▼****Algebra****►****11-XX Number theory****►****12-XX Field theory and polynomials****►****13-XX Commutative rings and algebras****►****14-XX Algebraic geometry****►****15-XX Linear and multilinear algebra; matrix theory****▼****16-XX Associative rings and algebras****►****16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****16Bxx General and miscellaneous****►****16Dxx Modules, bimodules and ideals****►****16Exx Homological methods****►****16Gxx Representation theory of rings and algebras**- 16H05 Orders and arithmetic, separable algebras, Azumaya algebras
**►****16Kxx Division rings and semisimple Artin rings****►****16Lxx Local rings and generalizations****►****16Nxx Radicals and radical properties of rings****►****16Pxx Chain conditions, growth conditions, and other forms of finiteness****►****16Rxx Rings with polynomial identity****►****16Sxx Rings and algebras arising under various constructions****►****16Uxx Conditions on elements****►****16Wxx Rings and algebras with additional structure****►****16Yxx Generalizations**- 16Z05 Computational aspects of associative rings

**►****17-XX Nonassociative rings and algebras****▼****18-XX Category theory; homological algebra****▼****18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****18Axx General theory of categories and functors****▼****18Bxx Special categories**- 18B05 Category of sets, characterizations
- 18B10 Category of relations, additive relations
- 18B15 Embedding theorems, universal categories
- 18B20 Categories of machines, automata, operative categories
- 18B25 Topoi
- 18B30 Categories of topological spaces and continuous mappings
- 18B35 Preorders, orders and lattices (viewed as categories)
- 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
- 18B99 None of the above, but in this section

**▼****18Cxx Categories and theories**- 18C05 Equational categories
- 18C10 Theories (e.g. algebraic theories), structure, and semantics
- 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
- 18C20 Algebras and Kleisli categories associated with monads
- 18C30 Sketches and generalizations
- 18C35 Accessible and locally presentable categories
- 18C50 Categorical semantics of formal languages
- 18C99 None of the above, but in this section

**▼****18Dxx Categories with structure**- 18D05 Double categories,
*2*-categories, bicategories and generalizations - 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
- 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
- 18D20 Enriched categories (over closed or monoidal categories)
- 18D25 Strong functors, strong adjunctions
- 18D30 Fibered categories
- 18D35 Structured objects in a category (group objects, etc.)
- 18D50 Operads
- 18D99 None of the above, but in this section

- 18D05 Double categories,
**►****18Exx Abelian categories****►****18Fxx Categories and geometry****►****18Gxx Homological algebra**

**►****19-XX***K*-theory**▼****20-XX Group theory and generalizations****►****20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****20Axx Foundations****▼****20Bxx Permutation groups**- 20B05 General theory for finite groups
- 20B07 General theory for infinite groups
- 20B10 Characterization theorems
- 20B15 Primitive groups
- 20B20 Multiply transitive finite groups
- 20B22 Multiply transitive infinite groups
- 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
- 20B27 Infinite automorphism groups
- 20B30 Symmetric groups
- 20B35 Subgroups of symmetric groups
- 20B40 Computational methods
- 20B99 None of the above, but in this section

**►****20Cxx Representation theory of groups****►****20Dxx Abstract finite groups****▼****20Exx Structure and classification of infinite or finite groups**- 20E05 Free nonabelian groups
- 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
- 20E07 Subgroup theorems; subgroup growth
- 20E08 Groups acting on trees
- 20E10 Quasivarieties and varieties of groups
- 20E15 Chains and lattices of subgroups, subnormal subgroups
- 20E18 Limits, profinite groups
- 20E22 Extensions, wreath products, and other compositions
- 20E25 Local properties
- 20E26 Residual properties and generalizations
- 20E28 Maximal subgroups
- 20E32 Simple groups
- 20E34 General structure theorems
- 20E36 General theorems concerning automorphisms of groups
- 20E42 Groups with a
*BN*-pair; buildings - 20E45 Conjugacy classes
- 20E99 None of the above, but in this section

**►****20Fxx Special aspects of infinite or finite groups****►****20Gxx Linear algebraic groups (classical groups)****►****20Hxx Other groups of matrices****▼****20Jxx Connections with homological algebra and category theory****►****20Kxx Abelian groups**- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
**►****20Mxx Semigroups****▼****20Nxx Other generalizations of groups**- 20P05 Probabilistic methods in group theory

**►****Analysis****►****Differential Equations****►****Transformations****►****Geometry****►****Statistics****►****Applied Mathematics****►****Didactics**

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