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 commutative ring theory, the notion of Gorenstein rings has been studied widely. For rings
having finite Krull dimension, Bass showed the characterization of Gorenstein rings as rings …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …

Given a semidualizing module C over a commutative Noetherian ring, Holm and Jørgensen
[Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

This paper generalize the idea of the authors in\cite {Bennis and Mahdou1}. Namely, we
define and study a particular case of modules with Gorenstein projective, injective, and flat …