| 16-XX | | Prev: 15 | Up: Top | Next: 17 | |
| Associative rings and algebras | |
| {For the commutative case, see 13-XX} |
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 (must also be assigned at least one classification number from Section 01)
| 16-04 |
Explicit machine computation and programs (not the theory of computation or programming)
| 16-06 |
Proceedings, conferences, collections, etc.
| |
16Bxx |
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
| |
16Dxx |
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]
[xref: 18G05]
| 16D50 |
Injective modules, self-injective rings [See also 16L60]
[xref: 16L60, 18G05]
| 16D60 |
Simple and semisimple modules, primitive rings and ideals
[xref: 16N60]
| 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]; module theory in a category-theoretic context; Morita equivalence and duality
| 16D99 |
None of the above, but in this section
| |
16Exx |
Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}
[xref: 18Gxx]
| 16E05 |
Syzygies, resolutions, complexes
[xref: 18G10]
| 16E10 |
Homological dimension
[xref: 18G20]
| 16E20 |
Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50]
[xref: 18F25, 18F30, 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
[xref: 06E20]
| 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
| |
16Gxx |
Representation theory of rings and algebras
[xref: 16D90]
| 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]
[xref: 06E20]
| 16G50 |
Cohen-Macaulay modules
[xref: 16D80]
| 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]
[xref: 11R34, 11R54, 11S25, 11S45, 12G05, 16G30]
| |
16Kxx |
Division rings and semisimple Artin rings [See also 12E15, 15A30]
[xref: 11R54, 11S45, 12E15]
| 16K20 |
Finite-dimensional {For crossed products, see 16S35}
| 16K40 |
Infinite-dimensional and general
| 16K50 |
Brauer groups [See also 12G05, 14F22]
[xref: 12G05, 14F22]
| 16K99 |
None of the above, but in this section
| |
16Lxx |
Local rings and generalizations
| 16L30 |
Noncommutative local and semilocal rings, perfect rings
| 16L60 |
Quasi-Frobenius rings [See also 16D50]
[xref: 16D50]
| 16L99 |
None of the above, but in this section
| |
16Nxx |
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
| |
16Pxx |
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], Krull dimension
| 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
| |
16Rxx |
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
| |
16Sxx |
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]
[xref: 17B35]
| 16S32 |
Rings of differential operators [See also 13N10, 32C38]
[xref: 13N10, 32C38]
| 16S34 |
Group rings [See also 20C05, 20C07], Laurent polynomial rings
[xref: 20C05, 20C07]
| 16S35 |
Twisted and skew group rings, crossed products
| 16S36 |
Ordinary and skew polynomial rings and semigroup rings [See also 20M25]
[xref: 20M25]
| 16S37 |
Quadratic and Koszul algebras
| 16S38 |
Rings arising from non-commutative algebraic geometry
| 16S40 |
Smash products of general Hopf actions [See also 16W30]
[xref: 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]
[xref: 32G05]
| 16S90 |
Maximal ring of quotients, torsion theories, radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}
[xref: 16D90, 18E40]
| 16S99 |
None of the above, but in this section
| |
16Uxx |
Conditions on elements
| 16U10 |
Integral domains
[xref: 16N60]
| 16U20 |
Ore rings, multiplicative sets, Ore localization
[xref: 16P50, 16P60]
| 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
| |
16Wxx |
Rings and algebras with additional structure
| 16W10 |
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
[xref: 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]; rings, modules, etc. on which these act
[xref: 16S40, 57T05, 81R50]
| 16W35 |
Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
[xref: 17B37, 20G42]
| 16W50 |
Graded rings and modules
[xref: 13A02]
| 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]
[xref: 13Jxx]
| 16W70 |
Filtered rings; filtrational and graded techniques
| 16W80 |
Topological and ordered rings and modules [See also 06F25, 13Jxx]
[xref: 13Jxx]
| 16W99 |
None of the above, but in this section
| |
16Yxx |
Generalizations {For nonassociative rings, see 17-XX}
| 16Y30 |
Near-rings [See also 12K05]
[xref: 12K05, 51J20]
| 16Y60 |
Semirings [See also 12K10]
[xref: 12K10, 20M25]
| 16Y99 |
None of the above, but in this section
| |
16Z05 |
Computational aspects of associative rings [See also 68W30]
[xref: 68W30]
| |