Mathematical Sciences Classification System

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
    None of the above but in this section
  • General and miscellaneous
  • Modules, bimodules and ideals
  • Homological methods
    {For commutative rings, see 13Dxx; for general categories, see 18Gxx}
  • Representation theory of rings and algebras
  • Algebras and orders
    {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30}
  • Division rings and semisimple Artin rings
    [See also 12E15, 15A30]
  • Local rings and generalizations
  • Radicals and radical properties of rings
  • Chain conditions, growth conditions, and other forms of finiteness
  • Rings with polynomial identity
  • Rings and algebras arising under various constructions
  • Hopf algebras, quantum groups and related topics
  • Conditions on elements
  • Rings and algebras with additional structure
  • Generalizations
    {For nonassociative rings, see 17-XX}
  • Computational aspects of associative rings

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