Finiteness criteria in Gorenstein homological algebra

Abstract

In this paper, we examine the class of modules of finite Gorenstein projective dimension and study approximations of modules in that class by modules which are either Gorenstein projective or else have finite projective dimension. We also examine the relevance of complete cohomology in the study of modules of finite Gorenstein projective dimension and obtain, over group rings, such a finiteness criterion that involves only complete cohomology.