We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …

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 …

Given an artin algebra $\Lambda $ with an idempotent element $ a $ we compare the
algebras $\Lambda $ and $ a\Lambda a $ with respect to Gorensteinness, singularity …

An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes
of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by …

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 …

An Artin algebra is by definition virtually Gorenstein if the class of modules which are right
orthogonal (with respect to $\operatorname {Ext}^*(-,-) $) to all Gorenstein projective …

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 show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

We give a classification of all exact structures on a given idempotent complete additive
category. Using this, we investigate the structure of an exact category with finitely many …

We prove a generalization of the stability for Gorenstein categories in [36] and [24]; and
show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other …