Cohen-Macaulay

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

Cohen-Macaulay (not comparable)

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 ${\displaystyle M}$ over a noetherian ring) Such that all localizations of ${\displaystyle M}$ at maximal ideals contained in the support of ${\displaystyle M}$ are either Cohen-Macaulay or trivial.
4. (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.