Cohen-Macaulay module

A module M over a ring R is a Cohen-Macaulay module if its depth is defined and equals its Krull dimension. A ring is said to be Cohen-Macaulay (or just C-M) if it is a Cohen-Macaulay module viewed as a module over itself.

Cohen-Macaulay rings are used extensively in combinatorial geometry and commutative ring theory, and has applications to algebraic geometryMathworldPlanetmathPlanetmath as well. For instance, a variety all of whose local ringsMathworldPlanetmath are Cohen-Macaulay has, in a sense, nicer behaviour than an arbitrary singular variety.

Title Cohen-Macaulay module
Canonical name CohenMacaulayModule
Date of creation 2013-03-22 14:14:58
Last modified on 2013-03-22 14:14:58
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Definition
Classification msc 13C14
Classification msc 16E65
Defines Cohen-Macaulay ring
Defines C-M module
Defines C-M ring