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**►****Foundations****▼****Algebra****►****11-XX Number theory****►****12-XX Field theory and polynomials****▼****13-XX Commutative rings and algebras****►****13-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****▼****13Axx General commutative ring theory**- 13A02 Graded rings
- 13A05 Divisibility
- 13A10 Radical theory
- 13A15 Ideals; multiplicative ideal theory
- 13A18 Valuations and their generalizations
- 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 - 13A50 Actions of groups on commutative rings; invariant theory
- 13A99 None of the above, but in this section

**►****13Bxx Ring extensions and related topics****▼****13Cxx Theory of modules and ideals**- 13C05 Structure, classification theorems
- 13C10 Projective and free modules and ideals
- 13C11 Injective and flat modules and ideals
- 13C12 Torsion modules and ideals
- 13C13 Other special types
- 13C14 Cohen-Macaulay modules
- 13C15 Dimension theory, depth, related rings (catenary, etc.)
- 13C20 Class groups
- 13C40 Linkage, complete intersections and determinantal ideals
- 13C99 None of the above, but in this section

**►****13Dxx Homological methods****►****13Exx Chain conditions, finiteness conditions****►****13Fxx Arithmetic rings and other special rings**- 13G05 Integral domains
**►****13Hxx Local rings and semilocal rings****►****13Jxx Topological rings and modules**- 13K05 Witt vectors and related rings
- 13L05 Applications of logic to commutative algebra
**►****13Mxx Finite commutative rings****▼****13Nxx Differential algebra****►****13Pxx Computational aspects of commutative algebra**

**►****14-XX Algebraic geometry****►****15-XX Linear and multilinear algebra; matrix theory****►****16-XX Associative rings and algebras****►****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****►****18Cxx Categories and theories****▼****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**- 18G05 Projectives and injectives
- 18G10 Resolutions; derived functors
- 18G15 Ext and Tor, generalizations, Künneth formula
- 18G20 Homological dimension
- 18G25 Relative homological algebra, projective classes
- 18G30 Simplicial sets, simplicial objects (in a category)
- 18G35 Chain complexes
- 18G40 Spectral sequences, hypercohomology
- 18G50 Nonabelian homological algebra
- 18G55 Homotopical algebra
- 18G60 Other (co)homology theories
- 18G99 None of the above, but in this section

**►****19-XX***K*-theory**▼****20-XX Group theory and generalizations****►****20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****20Axx Foundations****►****20Bxx Permutation groups****►****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**- 20H05 Unimodular groups, congruence subgroups
- 20H10 Fuchsian groups and their generalizations
- 20H15 Other geometric groups, including crystallographic groups
- 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

**▼****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****►****22-XX Topological groups, Lie groups****►****26-XX Real functions****►****28-00 Measure and integration****►****30-XX Functions of a complex variable****▼****31-XX Potential theory****►****32-XX Several complex variables and analytic spaces****►****33-XX Special functions (EDD 000 deals with the properties of functions as functions)**

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

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