Maximal Cohen-Macaulay tensor products and vanishing of Ext modules

Abstract

In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext modules. One of the applications shows that the Auslander-Reiten conjecture holds for Cohen-Macaulay normal rings.

9 pages, to appear in the Bulletin of the London Mathematical Society