|
16-XX
|
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,
16E10}
[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]
|
|
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
16G60]
|
|
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}
|
|
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
|
|
16Gxx
|
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]
|
|
16Kxx
|
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
|
|
16Lxx
|
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
|
|
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]
|
|
16S32
|
Rings of differential operators
[See also
13N10,
32C38]
|
|
16S34
|
Group rings
[See also
20C05,
20C07],
Laurent polynomial rings
|
|
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
|
|
16Uxx
|
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
|
|
16Wxx
|
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
57T05,
16S30,
16S40];
rings, modules, etc.
On which these act
|
|
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,
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
13Jxx]
|
|
16W99
|
None of the above, but in this section
|
|
16Yxx
|
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]
|