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 …

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 …

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 …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module of …

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-
injective) modules which are special Gorenstein projective (resp. Gorenstein injective) …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …

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 …

Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-
module. The notion grade of M, grade M, has been introduced by Rees as the least integer …

We show that over a right coherent left perfect ring R, a complex C of left R-modules is
Gorenstein projective if and only if C m is Gorenstein projective in R-Mod for all m∈ ℤ …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …