Sather-Wagstaff et al. proved in [8](S. Sather-Wagsta, T. Sharif and D. White, Stability of
Gorenstein categories, J. Lond. Math. Soc.(2), 77 (2)(2008), 481–502) that iterating the …

A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …

Abstract A left R-module M is called two-degree strongly Gorenstein flat if there exists an
exact sequence⋯⟶ D 1⟶ D 0⟶ D− 1⟶ D− 2⟶⋯ of strongly Gorenstein flat left R-modules …

We first introduce in the paper the W_F-Gorenstein modules to establish the following Foxby
equivalence: \xymatrix@C=80ptG(F)∩A_C\ar@\lt0.5ex>r^C⊗_R-\amp\,\,\,\,G(W_F)\ar@\lt0 …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

Let be a class of left R-modules that contains all projective left R-modules. We study a kind
of stability of-Gorenstein projective modules and settle in affirmative the following question …

Projectively coresolved Gorenstein flat modules were introduced recently by Saroch and
Stovicek and were shown to be Gorenstein projective. While the relation between …

In this paper, we introduce the concepts of Gorenstein FI-injective and Gorenstein FI-flat
modules and we are concerned with the stability of the class of Gorenstein FI-flat modules …

The purpose of this paper is to give, via totally different techniques, an alternate proof to the
main theorem of [18] in the category of modules over an arbitrary ring R. In effect, we prove …

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 …