Gorenstein‐projective module is an important research topic in relative homological algebra,
representation theory of algebras, triangulated categories, and algebraic geometry …

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 determine all the strongly complete projective resolutions, and all the strongly
Gorenstein projective modules, over upper triangular matrix artin algebras. In particular, we …

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 …

Let A be an Artin algebra, M be a Gorenstein projective A-module and B= End AM. We give
a characterization of modules on B and show that if A is Ω 2-representation-finite, then B is …

Let RR be an Artin algebra. Under certain Auslander‐type conditions, we give some
equivalent characterizations of (weakly) Gorenstein algebras in terms of the properties of …

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 prove that a certain eventually homological isomorphism between module categories
induces triangle equivalences between their singularity categories, Gorenstein defect …

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule
SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete …

We find sufficient and necessary conditions for the category of Gorenstein projective
modules of an artin algebra being an abelian category, and give another proof for the …