One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

We give a sufficient condition for the class of Gorenstein injective modules be precovering: if
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …

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 …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

Ding injective modules Page 1 Ding injective modules Alina Iacob Department of
Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA ABSTRACT We …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …

Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein
cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R …

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 introduce the notion of ω-Gorenstein modules, where ω is a faithfully balanced self-
orthogonal module. This gives a common generalization of both Gorenstein projective …

In this article, we prove that Gorenstein projectivity and injectivity with respect to a
semidualizing module are preserved under Frobenius extensions. Furthermore, we obtain …