Mathematics Subject Classification 1991

16-XX Associative rings and algebras, {For the commutative case, See 13-XX} ( 0 Dok.)

• 16-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 16-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 16-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 16-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 16-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 16-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 16Bxx General and miscellaneous ( 0 Dok. )
• 16B50 Category-theoretic methods and results (except as in 16D90, 16E10), See also {18-XX} ( 0 Dok.)
• 16B70 Applications of logic, See also {03Cxx} ( 0 Dok.)
• 16B99 None of the above but in this section ( 0 Dok.)
• 16Dxx Modules, bimodules and ideals ( 0 Dok. )
• 16D10 General module theory ( 0 Dok.)
• 16D15 1-sided ideals ( 0 Dok.)
• 16D20 Bimodules ( 0 Dok.)
• 16D25 2-sided ideals ( 0 Dok.)
• 16D30 Maximal and prime 2-sided ideals, See also {16N60, 16D60}, simple rings (except as in 16Kxx) ( 0 Dok.)
• 16D40 Free, projective, and flat modules and ideals, See Also {18G05, 19A13} ( 0 Dok.)
• 16D50 Injective modules, self-injective rings, See also {16L60, 18G05} ( 0 Dok.)
• 16D60 Simple and semisimple modules, primitive rings and ideals ( 0 Dok.)
• 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation ( 0 Dok.)
• 16D80 Other classes of modules and ideals, See also {16G60} ( 0 Dok.)
• 16D90 Module categories, See also {16Exx, 16Gxx, 16S90}; module theory in a category-theoretic context; Morita equivalence and duality ( 0 Dok.)
• 16D99 None of the above but in this section ( 0 Dok.)
• 16Exx Homological methods and results, See also {18Gxx} ( 0 Dok. )
• 16E10 Homological dimension ( 0 Dok.)
• 16E20 Grothendieck groups, $K$-theory, etc., See also {18F30, 19-XX} ( 0 Dok.)
• 16E30 Homological functors on modules ( 0 Dok.)
• 16E40 Hochschild and other homology and cohomology theories for rings ( 0 Dok.)
• 16E50 von Neumann regular rings and generalizations ( 0 Dok.)
• 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. ( 0 Dok.)
• 16E70 Other rings of low global or flat dimension ( 0 Dok.)
• 16E99 None of the above but in this section ( 0 Dok.)
• 16Gxx Representation theory of rings and algebras ( 0 Dok. )
• 16G10 Representations of Artinian rings ( 0 Dok.)
• 16G20 Representations of quivers and partially ordered sets ( 0 Dok.)
• 16G30 Representations of orders, lattices, algebras over commutative rings, See also {16H05} ( 0 Dok.)
• 16G50 Cohen-Macaulay modules ( 0 Dok.)
• 16G60 Representation type (finite, tame, wild, etc.) ( 0 Dok.)
• 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers ( 0 Dok.)
• 16G99 None of the above but in this section ( 0 Dok.)
• 16H05 Orders and arithmetic, separable algebras, Azumaya algebras, See also {11R52, 11R54, 11S45, 13A20} ( 0 Dok.)
• 16Kxx Division rings and semisimple Artin rings, See also {12E15, 15A30} ( 0 Dok. )
• 16K20 Finite-dimensional, {For Brauer group theory, See 12Gxx, 13A20; for crossed products, See 16S35} ( 0 Dok.)
• 16K40 Infinite-dimensional and general ( 0 Dok.)
• 16K99 None of the above but in this section ( 0 Dok.)
• 16Lxx Local rings and generalizations ( 0 Dok. )
• 16L30 Noncommutative local and semilocal rings, perfect rings ( 0 Dok.)
• 16L60 Quasi-Frobenius rings, See also {16D50} ( 0 Dok.)
• 16L99 None of the above but in this section ( 0 Dok.)
• 16Nxx Radicals and radical properties of rings ( 0 Dok. )
• 16N20 Jacobson radical, quasimultiplication ( 0 Dok.)
• 16N40 Nil and nilpotent radicals, sets, ideals, rings ( 0 Dok.)
• 16N60 Prime and semiprime rings, See also {16D30, 16D60, 16U10} ( 0 Dok.)
• 16N80 General radicals and rings, {For radicals in module categories, See 16S90} ( 0 Dok.)
• 16N99 None of the above but in this section ( 0 Dok.)
• 16Pxx Chain conditions, growth conditions, and other forms of finiteness ( 0 Dok. )
• 16P10 Finite rings and finite-dimensional algebras, {For semisimple, See 16K20; for commutative, See 11Txx, 13Mxx} ( 0 Dok.)
• 16P20 Artinian rings and modules ( 0 Dok.)
• 16P40 Noetherian rings and modules ( 0 Dok.)
• 16P50 Localization and Noetherian rings, See also {16U20} ( 0 Dok.)
• 16P60 Chain conditions on annihilators and summands: Goldie type conditions, See also {16U20}, Krull dimension ( 0 Dok.)
• 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence ( 0 Dok.)
• 16P90 Growth rate, Gelfand-Kirillov dimension ( 0 Dok.)
• 16P99 None of the above but in this section ( 0 Dok.)
• 16Rxx Rings with polynomial identity ( 0 Dok. )
• 16R10 $T$-ideals, identities, varieties of rings and algebras ( 0 Dok.)
• 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings ( 0 Dok.)
• 16R30 Trace rings and invariant theory ( 0 Dok.)
• 16R40 Identities other than those of matrices over commutative rings ( 0 Dok.)
• 16R50 Other kinds of identities (generalized polynomial, rational, involution) ( 0 Dok.)
• 16R99 None of the above but in this section ( 0 Dok.)
• 16Sxx Rings and algebras arising under various constructions ( 0 Dok. )
• 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) ( 0 Dok.)
• 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) ( 0 Dok.)
• 16S20 Centralizing and normalizing extensions ( 0 Dok.)
• 16S30 Universal enveloping algebras of Lie algebras See mainly{ 17B35} ( 0 Dok.)
• 16S32 Rings of differential operators, See also {13N10, 32C38} ( 0 Dok.)
• 16S34 Group rings, See also {20C05, 20C07}, Laurent polynomial rings ( 0 Dok.)
• 16S35 Twisted and skew group rings, crossed products ( 0 Dok.)
• 16S36 Ordinary and skew polynomial rings and semigroup rings, See also {20M25} ( 0 Dok.)
• 16S40 Smash products of general Hopf actions, See also {16W30} ( 0 Dok.)
• 16S50 Endomorphism rings: matrix rings, See also {15-XX} ( 0 Dok.)
• 16S60 Rings of functions, subdirect products, sheaves of rings ( 0 Dok.)
• 16S70 Extensions of rings by ideals ( 0 Dok.)
• 16S80 Deformations of rings, See also {14D15} ( 0 Dok.)
• 16S90 Maximal ring of quotients, torsion theories, radicals on module categories, See also {13D30, 18E40}, {For radicals of rings, See { 16Nxx}} ( 0 Dok.)
• 16S99 None of the above but in this section ( 0 Dok.)
• 16Uxx Conditions on elements (including elements of matrix rings, etc.) ( 0 Dok. )
• 16U10 Integral domains ( 0 Dok.)
• 16U20 Ore rings, multiplicative sets, Ore localization ( 0 Dok.)
• 16U30 Divisibility, noncommutative UFDs ( 0 Dok.)
• 16U50 Algebraicity and local finiteness, See also {16N40} ( 0 Dok.)
• 16U60 Units, groups of units, general linear groups ( 0 Dok.)
• 16U70 Center, normalizer (invariant elements) ( 0 Dok.)
• 16U80 Generalizations of commutativity ( 0 Dok.)
• 16U99 None of the above but in this section ( 0 Dok.)
• 16Wxx Rings and algebras with additional structure ( 0 Dok. )
• 16W10 Rings with involution: Lie, Jordan and other nonassociative structures, See also {17B60, 17C50, 46Kxx} ( 0 Dok.)
• 16W20 Automorphisms and endomorphisms, actions of groups and semigroups and their fixed rings ( 0 Dok.)
• 16W25 Derivations, actions of Lie algebras ( 0 Dok.)
• 16W30 Coalgebras, bialgebras, Hopf algebras, See also {57T05, 16S30-- 16S40}; rings, modules, etc. on which these act ( 0 Dok.)
• 16W50 Graded rings and modules ( 0 Dok.)
• 16W55 ``Super'' (or ``skew'') structure, See also {17A70, 17B70, 17C70}, {For exterior algebras, See { 15A75}; for Clifford algebras, See 11E88, 15A66} ( 0 Dok.)
• 16W60 Filtrations and valuations, generalizations of Euclidean algorithm, completions, formal power series and related constructions, See also {13Jxx} ( 0 Dok.)
• 16W80 Topological and ordered rings and modules, See also {13Jxx} ( 0 Dok.)
• 16W99 None of the above but in this section ( 0 Dok.)
• 16Yxx Generalizations, {For nonassociative rings, See 17-xx} ( 0 Dok. )
• 16Y30 Near-rings, See also {12K05} ( 0 Dok.)
• 16Y60 Semirings, See also {12K10} ( 0 Dok.)
• 16Y99 None of the above but in this section ( 0 Dok.)