![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
The long-standing Auslander and Reiten Conjecture states that a finitely generated module over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors, including Avramov, Buchweitz, Iyengar, Jorgensen, Nasseh, Sather-Wagstaff, and Şega, have studied a possible counterpart of the conjecture, or question, for commutative rings in terms of the vanishing of Tor. This has led to the notion of Tor-persistent rings. Our main result shows that the class of Tor-persistent local rings is closed under a number of standard procedures in ring theory.
Acknowledgments
We thank Avramov, Iyengar, Nasseh, and Sather-Wagstaff for useful comments and for making their article [Citation5] available to us. Part of this work was completed when Holm visited West Virginia University in March 2018. He is grateful for the kind hospitality of the WVU Department of Mathematics.
Notes
1 Note that this work is announced under the different title Vanishing of endohomology over local rings in [Citation6].