On modules with self Tor vanishing
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On modules with self Tor vanishing. / Celikbas, Olgur; Holm, Henrik.
In: Communications in Algebra, Vol. 48, No. 10, 2020, p. 4149-4154.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On modules with self Tor vanishing
AU - Celikbas, Olgur
AU - Holm, Henrik
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - G-dimension
KW - projective dimension
KW - Tor-persistent ring
KW - vanishing of Tor
UR - http://www.scopus.com/inward/record.url?scp=85085031073&partnerID=8YFLogxK
U2 - 10.1080/00927872.2020.1756311
DO - 10.1080/00927872.2020.1756311
M3 - Journal article
AN - SCOPUS:85085031073
VL - 48
SP - 4149
EP - 4154
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 10
ER -
ID: 242414901