We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

In this paper, we prove that the global Gorenstein projective dimension of a ring $ R $ is
equal to the global Gorenstein injective dimension of $ R $ and that the global Gorenstein …

The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …

In this paper, we study Gorenstein injective, projective, and flat dimensions over a Cohen-
Macaulay local ring R admitting a dualizing module. In particular, we characterize these …

In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …

Let R be a Gorenstein ring. We prove that if I is an ideal of R such that R/I is a semi-simple
ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein …

The Chouinard formula for the injective dimension of a module over a noetherian ring is
extended to Gorenstein injective dimension. Specifically, if $ M $ is a module of finite …

Throughout this paper, if not specified otherwise, R denotes an associative ring with identity
and all modules are unital left R-modules. Every result given for left modules has a …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is
not yet known whether the category GF (R) of Gorenstein flat modules over a ring R is …