In the paper, it is proven that every object in C (R-GProj) has a special C (R-Proj)-
preenvelope, and then some adjoints in homotopy categories related to Gorenstein …

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 …

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 …

Let X be a class of right R-modules that contains all projective right R-modules. The notion of
X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi (X-Gorenstein …

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 …

In this paper, we introduce the notion of Gorenstein quasi-resolving subcategories (denoted
by $\mathcal {GQR} _ {\mathcal {X}}(\mathcal {A}) $) in term of quasi-resolving subcategory …

Abstract Let $\mathcal {V, W} $ be two classes of modules. In this paper, we introduce and
study $\mathcal {VW} $-Gorenstein complexes as a common generalization of $\mathcal {W} …

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 …

In this paper, we generalize the notion of Gorenstein projective modules. Namely, we
introduce X-Gorenstein projective modules, where X is a class of modules that contains all …

DERIVED CATEGORY WITH RESPECT TO GORENSTEIN AC-PROJECTIVE MODULES Tianya
Cao, Zhongkui Liu and Xiaoyan Yang Abstract 1. Introduc Page 1 TY CAO, ZK LIU AND XY …