Let be a left Noetherian ring satisfying the Auslander condition. It is proven that a left-module
is Gorenstein injective if and only if is strongly cotorsion and for any injective left-module; a …

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 …

For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules
is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective …

We study some homological properties of Gorenstein FP∞-injective modules, and we prove
(1) a ring R is not necessarily coherent if every Gorenstein FP∞-injective R-module is …

In this note, it is proven that if R is a right noetherian ring with id R o R<∞ and E xt R i≥ 1
(M, F)= 0 for any left R-module F with finite flat dimension, then M is Gorenstein projective; if …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

The aim of this paper is to characterize $ n $-Gorenstein rings in terms of Gorenstein
injective modules and the Ext functor. We will show that if $ R $ is a left and right noetherian …

We prove that the class of Gorenstein injective modules is both enveloping and covering
over a two sided noetherian ring such that the character modules of Gorenstein injective …

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every
acyclic complex of injective modules is totally acyclic. We extend this characterization, which …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …