Auslander and Bridger [Stable module theory, Memoirs of the American Mathematical
Society, No. 94, American Mathematical Society, Providence, RI, 1969] introduced 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 …

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 …

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 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 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

We show that any module admits a presentation as the quotient of a Gorenstein projective
module by a submodule which is itself right orthogonal, with respect to the standard Ext 1 …

We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

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 notions of torsion and torsion freeness have played a very important role in module
theory--particularly in the study of modules over integral domains. Furthermore, the use of …