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

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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 …

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 prove that for a Frobenius extension, a module over the extension ring is Gorenstein
projective if and only if its underlying module over the base ring is Gorenstein projective. For …

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 give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

An extension $ B\subset A $ of finite dimensional algebras is bounded if the $ B $-$ B $-
bimodule $ A/B $ is $ B $-tensor nilpotent, its projective dimension is finite and $\mathrm …

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 …

We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …