In this paper the authors investigate homological and homotopical aspects of a concept of
torsion which is general enough to cover torsion and cotorsion pairs in abelian categories …

We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …

We study Artin algebras Λ and commutative Noetherian complete local rings R in connection
with the following decomposition property of Gorenstein-projective modules: We show that …

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

Let A be an artin algebra. An A-module M will be said to be semi-Gorenstein-projective
provided that Ext i (M, A)= 0 for all i≥ 1. All Gorenstein-projective modules are semi …

Gorenstein derived categories are defined, and the relation with the usual derived
categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

Let be an Artin algebra. Under suitable conditions, we describe all the modules in⊥ Λ, and
obtain criteria for the Gorensteinness of Λ. As applications, we determine explicitly all the …