On stability of Gorenstein categories

A Xu, N Ding - Communications in Algebra, 2013 - Taylor & Francis
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 …

Notes on stability of Gorenstein categories

A Xu - Journal of Algebra and Its Applications, 2013 - World Scientific
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 …

Stability of Gorenstein categories

KA Sather-Wagstaff, T Sharif… - Journal of the London …, 2008 - Wiley Online Library
We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

Stability of Gorenstein classes of modules

S Bouchiba - Algebra Colloquium, 2013 - World Scientific
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 …

Stability of Gorenstein flat categories

G Yang, Z Liu - Glasgow Mathematical Journal, 2012 - cambridge.org
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 …

Recollements of stable categories of Gorenstein injective modules

Z Wang, T Mu, X Wang - Journal of Algebra and Its Applications, 2021 - World Scientific
Let A and B be rings, U a (B, A)-bimodule and T= A 0 UB be a triangular matrix ring. We first
give an explicit description for Gorenstein injective T-modules over the triangular matrix ring …

Stability of Gorenstein flat modules

S Bouchiba, M Khaloui - Glasgow Mathematical Journal, 2012 - cambridge.org
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 …

GORENSTEIN CATEGORIES 𝒢 (𝒳, 𝒴, 𝒵) AND DIMENSIONS

X Yang - The Rocky Mountain Journal of Mathematics, 2015 - JSTOR
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 …

Stability of Gorenstein flat categories with respect to a semidualizing module

Z Di, Z Liu, J Chen - 2015 - projecteuclid.org
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 …

Relative Gorenstein flat modules and dimension

D Bennis, R El Maaouy, JRG Rozas… - Communications in …, 2022 - Taylor & Francis
In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …