In this paper we introduce the notion of Gorenstein X-flat R-module and study a kind of
stability of the class of Gorenstein X-flat R-modules. A ring R is called right GXF-closed if the …

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 …

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 …

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 …

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 …

Let X be a class of left R-modules, Y be a class of right R-modules. In this article, we
introduce and study Gorenstein (X, Y)-flat modules as a common generalization of some …

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 …

This paper mainly study the stability of Gorenstein modules with respect to a semidualizing
module C (ie, Gorenstein C-projective, Gorenstein C-injective and Gorenstein C-flat …

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 …

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 …