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 …

The Ext-strongly Gorenstein projective modules Page 1 Turkish Journal of Mathematics Volume
39 Number 1 Article 6 1-1-2015 The Ext-strongly Gorenstein projective modules JIE REN Follow …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the
class Cogen M is always a covering class whenever M is a quasi-cotilting module. Some …

We introduce symmetric subcategories of abelian categories and show that the derived
category of the endomorphism ring of any good tilting module over a ring is a recollement of …

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 …

0 Introduction 611 1 Left derived extension functors 612 2 Gorenstein injective modules 616
3 Resolutions and resolvents 620 4 The existence of Gorenstein injective modules 623 5 …