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Words, grammatical forms and meanings linked to the ontology.

Cohen-Macaulay en · ADJ

Etymology

Named for Irvin Cohen and Francis Sowerby Macaulay, who proved unmixedness results for specific classes of rings, which Cohen-Macaulay rings generalize.

Meanings

  1. (not-comparable, of a finite module over a noetherian local ring, qualifier:commutative algebra) Such that its depth is equal to its Krull dimension.
  2. (not-comparable, of a noetherian local ring, qualifier:commutative algebra) Cohen-Macaulay as a module over itself.
  3. (not-comparable, of a module M over a noetherian ring, qualifier:commutative algebra) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.

wikipedia: Irvin Cohen · wikipedia: Francis Sowerby Macaulay