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For any ring R and any positive integer n, we prove that a left R-module is a Gorenstein n-
syzygy if and only if it is an n-syzygy. Over a left and right Noetherian ring, we introduce the …

Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

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

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

Journal of Algebra Strongly Gorenstein projective, injective and flat modules Page 1 Journal
of Algebra 320 (2008) 2659–2674 Contents lists available at ScienceDirect Journal of Algebra …

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 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 …

In this paper, we introduce and study (weak) pure-injective Gorenstein projective modules.
Let R be an Artin algebra. We prove that the category of weak pure-injective Gorenstein …

We give a sufficient condition for the class of Gorenstein injective modules be precovering: if
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …