For an integer N≥ 2 and three subcategories 𝒲, 𝒳, 𝒴 of modules, we study the notion of (𝒲,
𝒳, 𝒴)-Gorenstein N-complexes. We show that under certain hypotheses, an N-complex C is …

In this paper, we generalize the idea of Song, Zhao and Huang [Czechoslov. Math. J., 70,
483–504 (2020)] and introduce the notion of right (left) Gorenstein subcategory r G (C, D)(l G …

Let 𝒜 be an abelian category with enough projectives. In the category of 𝒜-complexes, we
introduce generalized Tate cohomology with respect to subcategories, and show that there …

In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to
a semidualizing bimodule $ _SC_R $, where R and S are arbitrary associative rings. We …

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 …

ABSTRACT Let 𝒲, 𝒴, 𝒳 be three classes of left R-modules. In this paper, we introduce and
study (𝒲, 𝒴, 𝒳)-Gorenstein complexes as a common generalization of completely 𝒲-resolved …

Abstract Let 𝒱, 𝒲, 𝒴, 𝒳 be four classes of modules. We introduce a notion of (𝒱, 𝒲, 𝒴, 𝒳)-
Gorenstein modules which unifies a number of well-known Gorenstein modules. Under …

In this paper, we establish some new Foxby equivalences between some Gorenstein
subcategories in the Auslander class 𝒜 C (R) and that in the Bass class ℬ C (S) in a general …

In this paper, we introduce strongly (X, Y, ZX, Y, Z)-Gorenstein modules, where X, Y, ZX, Y, Z
are additive full subcategories of R-\mathrm Mod M od. These modules provide a new …