Cohen-Macaulay
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English
Etymology
Named for Irvin Cohen and Francis Sowerby Macaulay, who proved unmixedness results for specific classes of rings, which Cohen-Macaulay rings generalize.
Adjective
Cohen-Macaulay (not comparable)
- (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
- (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
- (commutative algebra, of a module over a noetherian ring) Such that all localizations of at maximal ideals contained in the support of are either Cohen-Macaulay or trivial.
- (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.
