Let X be a class of right R-modules that contains all projective right R-modules. The notion of
X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi (X-Gorenstein …

In this paper, we introduce and study the notions of Gorenstein n-FP-injective and
Gorenstein n-flat complexes, which are special cases of Gorenstein FP-injective and …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

Let R be a Gorenstein ring. We prove that if I is an ideal of R such that R/I is a semi-simple
ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein …

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ n is Gorenstein flat
in R-Mod for all n∈ ℤ. Let 𝒮𝒢 stand for the class of strongly Gorenstein flat complexes. We …

Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has
finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope …

This paper generalize the idea of the authors in\cite {Bennis and Mahdou1}. Namely, we
define and study a particular case of modules with Gorenstein projective, injective, and flat …

In this note, we mainly discuss strongly Gorenstein hereditary rings. We prove that for any
ring, the class of SG-projective modules and the class of G-projective modules coincide if …

The notion of X-strongly Gorenstein projective module was defined. It was proved that a
module is X-Gorenstein projective if and only if it is a direct summand of some X …

For a left and right Noetherian ring R, we give some equivalent characterizations for RR
satisfying the Auslander condition in terms of the flat (resp. injective) dimensions of the terms …