## Mathematics Subject Classification – MSC2010

General reference works (handbooks, dictionaries, bibliographies, etc.) 30

Instructional exposition (textbooks, tutorial papers, etc.) 289

Research exposition (monographs, survey articles) 623

Explicit machine computation and programs (not the theory of computation or programming) 57

Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 3170

Homological functors on modules (Tor, Ext, etc.) 1478

(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc. (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 1730

Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 552

Representation type (finite, tame, wild, etc.) 1592

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 1343

Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 2113

Finite rings and finite-dimensional algebras [For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx] 2774

Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension 1767

Other kinds of identities (generalized polynomial, rational, involution) 969

Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 850

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 626

Torsion theories; radicals on module categories [See also 13D30, 18E40] [For radicals of rings, see 16Nxx] 1449

Center, normalizer (invariant elements) 1557