Auslander and Bridger [1] generalized finitely generated projective modules to modules of
Gorenstein dimension zero over two-sided Noetherian rings. After two decades, Enochs and …

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 …

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

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 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 …

In this paper, we introduce and study (weak) pure-injective Gorenstein projective modules.
Let R be an Artin algebra. We prove that the category of weak pure-injective Gorenstein …

Abstract Let Λ=\left () Λ=(AM 0 B) be an Artin algebra. In view of the characterization of
finitely generated Gorenstein injective Λ-modules under the condition that M is a …

Under semi-weak and weak compatibility conditions of bimodules, we establish necessary
and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with …

In this paper, we obtain necessary and sufficient conditions for all complete projective
resolutions over a Morita ring Δ (0, 0)(A, B, M, N)= AANBBMAB. As special cases, we get a …

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 …