On modules with self Tor vanishing

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 counte...

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Bibliographic Details
Published in:Communications in algebra 2020-10, Vol.48 (10), p.4149-4154
Main Authors: Celikbas, Olgur, Holm, Henrik
Format: Article
Language:English
Subjects:
Commutativity
G-dimension
Modules
projective dimension
Rings (mathematics)
Tor-persistent ring
vanishing of Tor
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2020.1756311