Suppose $ R $ is a $\mathbb {Q} $-Gorenstein $ F $-finite and $ F $-pure ring of prime
characteristic $ p> 0$. We show that if $ I\subseteq R $ is a compatible ideal (with all $ p^{-e} …

In\cite {Ouarghi}, the authors discuss the rings over which all modules are strongly
Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

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 …

In this paper, we introduce the notion of Gorenstein $(m, n) $-flat modules as an extension of
$(m, n) $-flat left $ R $-modules over a ring $ R $, where $ m $ and $ n $ are two fixed …

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 …

The notion of $2 $-almost Gorenstein ring is a generalization of the notion of almost
Gorenstein ring in terms of Sally modules of canonical ideals. In this paper, we deal with two …

Abstract Let 𝒱, 𝒲, 𝒴, 𝒳 be four classes of modules. We introduce a notion of (𝒱, 𝒲, 𝒴, 𝒳)-
Gorenstein modules which unifies a number of well-known Gorenstein modules. Under …

Let R⋉ M be a trivial extension of a ring R by an RR-bimodule M. Sufficient and necessary
conditions are established for Gorenstein flat-cotorsion modules over R⋉ M. More precisely …

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 …