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Navegando por la clasificación temática MSC 2000: 16 · Associative rings and algebras
 
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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