| 16-XX |
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Associative rings and algebras {For the commutative case, see 13-XX} |
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16-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras |
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16-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras |
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16-02 |
Research exposition (monographs, survey articles) pertaining to associative rings and algebras |
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16-03 |
History of associative rings and algebras [Consider also classification numbers from Section 01-XX] |
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16-04 |
Software, source code, etc. for problems pertaining to associative rings and algebras |
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16-06 |
Proceedings, conferences, collections, etc. pertaining to associative rings and algebras |
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16-11 |
Research data for problems pertaining to associative rings and algebras |
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16B50 |
Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18-XX] |
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16B70 |
Applications of logic in associative algebras [See also 03Cxx] |
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16B99 |
None of the above, but in this section |
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16D10 |
General module theory in associative algebras |
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16D20 |
Bimodules in associative algebras |
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16D25 |
Ideals in associative algebras |
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16D30 |
Infinite-dimensional simple rings (except as in 16Kxx) |
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16D40 |
Free, projective, and flat modules and ideals in associative algebras [See also 19A13] |
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16D50 |
Injective modules, self-injective associative rings [See also 16L60] |
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16D60 |
Simple and semisimple modules, primitive rings and ideals in associative algebras |
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16D70 |
Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
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16D80 |
Other classes of modules and ideals in associative algebras [See also 16G50] |
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16D90 |
Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality |
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16D99 |
None of the above, but in this section |
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16E05 |
Syzygies, resolutions, complexes in associative algebras |
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16E10 |
Homological dimension in associative algebras |
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16E20 |
Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50] |
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16E30 |
Homological functors on modules (Tor, Ext, etc.) in associative algebras |
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16E35 |
Derived categories and associative algebras |
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16E40 |
(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
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16E45 |
Differential graded algebras and applications (associative algebraic aspects) |
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16E50 |
von Neumann regular rings and generalizations (associative algebraic aspects) |
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16E60 |
Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. |
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16E65 |
Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
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16E99 |
None of the above, but in this section |
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16G10 |
Representations of associative Artinian rings |
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16G20 |
Representations of quivers and partially ordered sets |
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16G30 |
Representations of orders, lattices, algebras over commutative rings [See also 16Hxx] |
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16G50 |
Cohen-Macaulay modules in associative algebras |
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16G60 |
Representation type (finite, tame, wild, etc.) of associative algebras |
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16G70 |
Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
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16G99 |
None of the above, but in this section |
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16H05 |
Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) |
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16H10 |
Orders in separable algebras |
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16H15 |
Commutative orders |
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16H20 |
Lattices over orders |
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16H99 |
None of the above, but in this section |
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16K20 |
Finite-dimensional division rings {For crossed products, see 16S35} |
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16K40 |
Infinite-dimensional and general division rings |
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16K50 |
Brauer groups (algebraic aspects) [See also 12G05, 14F22] |
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16K99 |
None of the above, but in this section |
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16L30 |
Noncommutative local and semilocal rings, perfect rings |
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16L60 |
Quasi-Frobenius rings [See also 16D50] |
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16L99 |
None of the above, but in this section |
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16N20 |
Jacobson radical, quasimultiplication |
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16N40 |
Nil and nilpotent radicals, sets, ideals, associative rings |
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16N60 |
Prime and semiprime associative rings [See also 16D60, 16U10] |
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16N80 |
General radicals and associative rings {For radicals in module categories, see 16S90} |
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16N99 |
None of the above, but in this section |
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16P10 |
Finite rings and finite-dimensional associative algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} |
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16P20 |
Artinian rings and modules (associative rings and algebras) |
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16P40 |
Noetherian rings and modules (associative rings and algebras) |
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16P50 |
Localization and associative Noetherian rings [See also 16U20] |
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16P60 |
Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras) |
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16P70 |
Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) |
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16P90 |
Growth rate, Gelfand-Kirillov dimension |
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16P99 |
None of the above, but in this section |
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16R10 |
$T$-ideals, identities, varieties of associative rings and algebras |
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16R20 |
Semiprime p.i. rings, rings embeddable in matrices over commutative rings |
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16R30 |
Trace rings and invariant theory (associative rings and algebras) |
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16R40 |
Identities other than those of matrices over commutative rings |
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16R50 |
Other kinds of identities (generalized polynomial, rational, involution) |
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16R60 |
Functional identities (associative rings and algebras) |
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16R99 |
None of the above, but in this section |
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16S10 |
Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
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16S15 |
Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) |
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16S20 |
Centralizing and normalizing extensions |
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16S30 |
Universal enveloping algebras of Lie algebras [See mainly 17B35] |
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16S32 |
Rings of differential operators (associative algebraic aspects) [See also 13N10, 32C38] |
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16S34 |
Group rings [See also 20C05, 20C07], Laurent polynomial rings (associative algebraic aspects) |
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16S35 |
Twisted and skew group rings, crossed products |
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16S36 |
Ordinary and skew polynomial rings and semigroup rings [See also 20M25] |
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16S37 |
Quadratic and Koszul algebras |
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16S38 |
Rings arising from noncommutative algebraic geometry [See also 14A22] |
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16S40 |
Smash products of general Hopf actions [See also 16T05] |
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16S50 |
Endomorphism rings; matrix rings [See also 15-XX] |
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16S60 |
Associative rings of functions, subdirect products, sheaves of rings |
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16S70 |
Extensions of associative rings by ideals |
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16S80 |
Deformations of associative rings [See also 13D10, 14D15] |
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16S85 |
Associative rings of fractions and localizations [See also 13B30] |
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16S88 |
Leavitt path algebras |
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16S90 |
Torsion theories; radicals on module categories (associative algebraic aspects) [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} |
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16S99 |
None of the above, but in this section |
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16T05 |
Hopf algebras and their applications [See also 16S40, 57T05] |
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16T10 |
Bialgebras |
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16T15 |
Coalgebras and comodules; corings |
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16T20 |
Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] |
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16T25 |
Yang-Baxter equations |
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16T30 |
Connections of Hopf algebras with combinatorics [See also 05Exx] |
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16T99 |
None of the above, but in this section |
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16U10 |
Integral domains (associative rings and algebras) |
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16U20 |
Ore rings, multiplicative sets, Ore localization |
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16U30 |
Divisibility, noncommutative UFDs |
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16U40 |
Idempotent elements (associative rings and algebras) |
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16U60 |
Units, groups of units (associative rings and algebras) |
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16U70 |
Center, normalizer (invariant elements) (associative rings and algebras) |
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16U80 |
Generalizations of commutativity (associative rings and algebras) |
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16U90 |
Generalized inverses (associative rings and algebras) |
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16U99 |
None of the above, but in this section |
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16W10 |
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] |
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16W20 |
Automorphisms and endomorphisms |
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16W22 |
Actions of groups and semigroups; invariant theory (associative rings and algebras) |
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16W25 |
Derivations, actions of Lie algebras |
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16W50 |
Graded rings and modules (associative rings and algebras) |
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16W55 |
"Super'' (or "skew'') structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66} |
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16W60 |
Valuations, completions, formal power series and related constructions (associative rings and algebras) [See also 13Jxx] |
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16W70 |
Filtered associative rings; filtrational and graded techniques |
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16W80 |
Topological and ordered rings and modules [See also 06F25, 13Jxx] |
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16W99 |
None of the above, but in this section |
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16Y20 |
Hyperrings |
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16Y30 |
Near-rings [See also 12K05] |
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16Y60 |
Semirings [See also 12K10] |
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16Y80 |
$\Gamma$ and fuzzy structures |
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16Y99 |
None of the above, but in this section |
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16Z05 |
Computational aspects of associative rings (general theory) [See also 68W30] |
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16Z10 |
Gröbner-Shirshov bases |
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16Z99 |
None of the above, but in this section |
