On weakly Gorenstein algebras

Abstract

We prove that algebras are left weakly Gorenstein in case the subcategory ${}^{\perp }A\cap {\Omega }^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over representation-finite algebras. We also give a proof of the Auslander-Reiten conjecture for such algebras.

The results of this article are now included in arXiv:1608.04212

References in corpus (2)

• Auslander correspondence
• Gorenstein Homological Algebra of Artin Algebras