We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein
projective, then its underlying module over the base ring is Gorenstein projective; the …

Abstract It was recently proved ([12]) that the class of Gorensteininjective left R-modules is
both covering and enveloping over a two sided noetherian ring R with the property that the …

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 …

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 …

Let R be a commutative Noetherian ring. In this paper, we study those finitely generated R-
modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a …

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 …

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 …

In this article, the concept of Gorenstein FP-injective modules and some related known
results are generalized to Gorenstein FP-injective complexes. Moreover, some new …

Let ℰ be an injectively resolving subcategory of left R-modules. We study a particular case of
ℰ-Gorenstein injective and flat modules, called strongly ℰ-Gorenstein injective and flat …

Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective
preenvelopes for finite R-modules is known (it was proved using duality arguments). In the …