Gorenstein homological dimensions and Auslander categories

Abstract

In this paper, we study Gorenstein projective and flat modules over a Noetherian ring R. For an R-module M, we show that Gorenstein projective dimension of M is finite if and only if Gorenstein flat dimension of M is finite provided the Krull dimension of R is finite. Moreover, in the case that R is local, we prove that Gorenstein projective dimension of an R-module M is finite if and only if R ˆ ⊗ R M belongs to the Auslander category of R ˆ .