Biblioteca Dr. Antonio Monteiro · Catálogo | |
16 | Associative rings and algebras | ||
16-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) | ||
16-01 | Instructional exposition (textbooks, tutorial papers, etc.) | ||
16-02 | Research exposition (monographs, survey articles) | ||
16-03 | Historical | ||
16-04 | Explicit machine computation and programs (not the theory of computation or programming) | ||
16-06 | Proceedings, conferences, collections, etc. | ||
16-99 | Associative rings and algebras (not classified at a more specific level) | ||
16B | General and miscellaneous | ||
16B50 | Category-theoretic methods and results (except as in 16D90) [See also 18-XX] | ||
16B70 | Applications of logic [See also 03Cxx] | ||
16B99 | None of the above, but in this section | ||
16D | Modules, bimodules and ideals | ||
16D10 | General module theory | ||
16D20 | Bimodules | ||
16D25 | Ideals | ||
16D30 | Infinite-dimensional simple rings (except as in 16Kxx) | ||
16D40 | Free, projective, and flat modules and ideals [See also 19A13] | ||
16D50 | Injective modules, self-injective rings [See also 16L60] | ||
16D60 | Simple and semisimple modules, primitive rings and ideals | ||
16D70 | Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation | ||
16D80 | Other classes of modules and ideals [See also 16G50] | ||
16D90 | Module categories [See also 16Gxx, 16S90] | ||
16D99 | None of the above, but in this section | ||
16E | Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx } | ||
16E05 | Syzygies, resolutions, complexes | ||
16E10 | Homological dimension | ||
16E20 | Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50] | ||
16E30 | Homological functors on modules (Tor, Ext, etc.) | ||
16E40 | (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) | ||
16E45 | Differential graded algebras and applications | ||
16E50 | von Neumann regular rings and generalizations | ||
16E60 | Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. | ||
16E65 | Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) | ||
16E99 | None of the above, but in this section | ||
16G | Representation theory of rings and algebras | ||
16G10 | Representations of Artinian rings | ||
16G20 | Representations of quivers and partially ordered sets | ||
16G30 | Representations of orders, lattices, algebras over commutative rings [See also 16H05] | ||
16G50 | Cohen-Macaulay modules | ||
16G60 | Representation type (finite, tame, wild, etc.) | ||
16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers | ||
16G99 | None of the above, but in this section | ||
16H05 | Orders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45] | ||
16K | Division rings and semisimple Artin rings [See also 12E15, 15A30] | ||
16K20 | Finite-dimensional {For crossed products, see 16S35} | ||
16K40 | Infinite-dimensional and general | ||
16K50 | Brauer groups [See also 12G05, 14F22] | ||
16K99 | None of the above, but in this section | ||
16L | 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 | ||
16N | Radicals and radical properties of rings | ||
16N20 | Jacobson radical, quasimultiplication | ||
16N40 | Nil and nilpotent radicals, sets, ideals, rings | ||
16N60 | Prime and semiprime rings [See also 16D60, 16U10] | ||
16N80 | General radicals and rings {For radicals in module categories, see 16S90} | ||
16N99 | None of the above, but in this section | ||
16P | Chain conditions, growth conditions, and other forms of finiteness | ||
16P10 | Finite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} | ||
16P20 | Artinian rings and modules | ||
16P40 | Noetherian rings and modules | ||
16P50 | Localization and Noetherian rings [See also 16U20] | ||
16P60 | Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20] | ||
16P70 | Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence | ||
16P90 | Growth rate, Gelfand-Kirillov dimension | ||
16P99 | None of the above, but in this section | ||
16R | Rings with polynomial identity | ||
16R10 | $T$-ideals, identities, varieties of rings and algebras | ||
16R20 | Semiprime p.i. rings, rings embeddable in matrices over commutative rings | ||
16R30 | Trace rings and invariant theory | ||
16R40 | Identities other than those of matrices over commutative rings | ||
16R50 | Other kinds of identities (generalized polynomial, rational, involution) | ||
16R99 | None of the above, but in this section | ||
16S | Rings and algebras arising under various constructions | ||
16S10 | 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 [See also 13N10, 32C38] | ||
16S34 | Group rings [See also 20C05, 20C07] | ||
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 non-commutative algebraic geometry | ||
16S40 | Smash products of general Hopf actions [See also 16W30] | ||
16S50 | Endomorphism rings; matrix rings [See also 15-XX] | ||
16S60 | Rings of functions, subdirect products, sheaves of rings | ||
16S70 | Extensions of rings by ideals | ||
16S80 | Deformations of rings [See also 13D10, 14D15] | ||
16S90 | Maximal ring of quotients, torsion theories, radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} | ||
16S99 | None of the above, but in this section | ||
16U | Conditions on elements | ||
16U10 | Integral domains | ||
16U20 | Ore rings, multiplicative sets, Ore localization | ||
16U30 | Divisibility, noncommutative UFDs | ||
16U60 | Units, groups of units | ||
16U70 | Center, normalizer (invariant elements) | ||
16U80 | Generalizations of commutativity | ||
16U99 | None of the above, but in this section | ||
16W | 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 | ||
16W25 | Derivations, actions of Lie algebras | ||
16W30 | Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05] | ||
16W35 | Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] | ||
16W50 | Graded rings and modules | ||
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 [See also 13Jxx] | ||
16W70 | Filtered 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 | ||
16Y | Generalizations {For nonassociative rings, see 17-XX} | ||
16Y30 | Near-rings [See also 12K05] | ||
16Y60 | Semirings [See also 12K10] | ||
16Y99 | None of the above, but in this section | ||
16Z05 | Computational aspects of associative rings [See also 68W30] | ||
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