We present and study the concept of m-periodic Gorenstein objects relative to a pair (A, B) of
classes of objects in an abelian category, as a generalization of m-strongly Gorenstein …

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 …

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

In this paper, we generalize the notion of Gorenstein projective modules. Namely, we
introduce X-Gorenstein projective modules, where X is a class of modules that contains all …

ABSTRACT Let R⊂ A be a Frobenius extension of rings. We prove that:(1) for any left A-
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …

We provide a simple proof for a recent result of Bravo, Gillespie and Hovey, showing that
over a left coherent ring for which the projective dimension of at right modules is finite, the …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a
semidualizing module to be dualizing in terms of special homological properties of module …