Abstract Let XX, UU and ZZ be classes of left R-modules, WW be a class of right R-modules
and X ⊆ UX⊆ U. In this paper, we investigate the relationship between Z Z-proper (resp. Z Z …

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 …

In this paper, weak Gorenstein projective, injective and flat modules are introduced and
investigated. A left R-module M is called weak Gorenstein projective if there exists an exact …

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

We prove that all Gorenstein projective modules are Gorenstein flat if and only each
Gorenstein projective module has finite Gorenstein flat dimension. As applications, some …

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 …

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 …

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 …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …