Cohen-Macaulay

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

Adjective

 * 1)  Such that its depth is equal to its Krull dimension.
 * 2)   as a module over itself.
 * 3)  Such that all localizations of $$M$$ at maximal ideals contained in the support of $$M$$ are either  or trivial.
 * 4)   as a module over itself.