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
  • 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 18G05, 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]; 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]
• 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
• 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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