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 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 …

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 …

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 …

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 basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

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 …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

Unlike the Gorenstein projective and injective dimensions, the majority of results on the
Gorenstein flat dimension have been established only over Noetherian (or coherent) rings …

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 …