Cohen-Macaulay

词源说明

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

释义

形容词adjective

1(commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
2(commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
3(commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
4(commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.