La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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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.
• 16-99 Associative rings and algebras (not classified at a more specific level)
• 16Bxx General and miscellaneous
• 16Dxx Modules, bimodules and ideals
• 16Exx Homological methods [For commutative rings, see 13Dxx; for general categories, see 18Gxx]
• 16Gxx Representation theory of rings and algebras
• 16H05 Orders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45]
• 16Kxx Division rings and semisimple Artin rings [See also 12E15, 15A30]
• 16Lxx Local rings and generalizations
• 16Nxx Radicals and radical properties of rings
• 16Pxx Chain conditions, growth conditions, and other forms of finiteness
• 16Rxx Rings with polynomial identity
• 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 [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 16S99
  • 16S38 Rings arising from non-commutative algebraic geometry [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 16S99
  • 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
• 16Wxx Rings and algebras with additional structure
• 16Yxx Generalizations [For nonassociative rings, see 17-XX]
• 16Z05 Computational aspects of associative rings [See also 68W30] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 16-04

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