Cohen-Macaulay

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)

2. (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
3. (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
5. (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.
6. (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.