By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

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 …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we
introduce the notions of strongly WP-Gorenstein, WI-Gorenstein and WF-Gorenstein …

We show that any module admits a presentation as the quotient of a Gorenstein projective
module by a submodule which is itself right orthogonal, with respect to the standard Ext 1 …

In basic homological algebra, projective, injective and flat modules play an important and
fundamental role. In this paper, we discuss some properties of Gorenstein projective …

Unless stated otherwise, throughout this paper all rings are associative with identity and all
modules are unitary modules. Let R be a ring. We denote by R-Mod (Mod-R) the category of …

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 …

We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of …