Let $ R $ be a left coherent ring. It is proven that if an $ R $-module $ M $ has a finite FP-
injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the …

The aim of this paper is two-fold. Given a recollement (T′, T, T ″, i*, i*, i!, j!, j*, j*), where
T′, T, T ″are triangulated categories with small coproducts and T is compactly generated …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

Foxby duality has proven to be an important tool in studying the category of modules over a
local Cohen-Macaulay ring admitting a dualizing module. Recently the notion of a semi …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

Recently, Gorenstein dimensions relative to a semidualizing module have been the subject
of numerous studies with interesting extensions of the classical homological dimensions …

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 introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules
over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order …