Abstract
AbstractLet be an Artin algebra. Under certain Auslander‐type conditions, we give some equivalent characterizations of (weakly) Gorenstein algebras in terms of the properties of Gorenstein projective modules and modules satisfying Auslander‐type conditions. As applications, we provide some support for several homological conjectures. In particular, we prove that if is left quasi‐Auslander, then is Gorenstein if and only if it is (left and) right weakly Gorenstein; and that if satisfies the Auslander condition, then is Gorenstein if and only if it is left or right weakly Gorenstein. This is a reduction of an Auslander–Reiten's conjecture, which states that is Gorenstein if satisfies the Auslander condition.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
