Cohen-macaulay dimension of modules over noetherian rings

Abstract

We extend a criterion of Gerko for a ring to be Cohen-Macaulay to arbitrary, not necessarily local, Noetherian rings. Our version reads as follows: The Noetherian ring R is Cohen-Macaulay if and only if, for all finitely generated R-modules M, CM-dimRM is finite. © 2005 Rocky Mountain Mathematics Consortium.