Let G (X) and G (Y) be Gorenstein subcategories induced by an admissible balanced pair
(X, Y) in an abelian category A. In this paper, we establish Gorenstein homological …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

In this paper, we study the Gorenstein (L, A)-projective resolution dimension of modules and
the left global Gorenstein (L, A)-projective dimension of rings in detail, where (L, A) …

Let 𝒜 be an abelian category and (𝒳, 𝒴) a pair of classes of objects in 𝒜. Inspired by
Bouchiba's work on generalized Gorenstein projective modules, we give a new way of …

In this paper we develop the homological properties of the Gorenstein $(\Le,\A) $-flat $ R $-
modules $\GF_ {(\Flat (R),\A)} $ proposed by Gillespie,\linebreak where the class …

Throughout this paper, if not specified otherwise, R denotes an associative ring with identity
and all modules are unital left R-modules. Every result given for left modules has a …

Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under
extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this …

We construct new complete cotorsion pairs in the categories of modules and chain
complexes over a Gorenstein ring $ R $, from the notions of Gorenstein homological …

We establish some relationships between Gorenstein AC-projective modules and
Gorenstein AC-flat modules. As applications, we obtain some new characterizations of …

In this paper, we study Gorenstein injective, projective, and flat dimensions over a Cohen-
Macaulay local ring R admitting a dualizing module. In particular, we characterize these …