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 …

We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …

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 …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

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 …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of …

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 $\Lambda $ be an arbitrary monomial algebra. We investigate the stable category
$\underline {\operatorname {Gproj}}^{\mathbb {Z}}\Lambda $ of graded Gorenstein …

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