On modules with self Tor vanishing

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On modules with self Tor vanishing. / Celikbas, Olgur; Holm, Henrik.

I: Communications in Algebra, Bind 48, Nr. 10, 2020, s. 4149-4154.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Celikbas, O & Holm, H 2020, 'On modules with self Tor vanishing', Communications in Algebra, bind 48, nr. 10, s. 4149-4154. https://doi.org/10.1080/00927872.2020.1756311

APA

Celikbas, O., & Holm, H. (2020). On modules with self Tor vanishing. Communications in Algebra, 48(10), 4149-4154. https://doi.org/10.1080/00927872.2020.1756311

Vancouver

Celikbas O, Holm H. On modules with self Tor vanishing. Communications in Algebra. 2020;48(10):4149-4154. https://doi.org/10.1080/00927872.2020.1756311

Author

Celikbas, Olgur ; Holm, Henrik. / On modules with self Tor vanishing. I: Communications in Algebra. 2020 ; Bind 48, Nr. 10. s. 4149-4154.

Bibtex

@article{e0f3299f7d53407683d6ad1bc3b7394e,
title = "On modules with self Tor vanishing",
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 {\c S}ega, 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.",
keywords = "G-dimension, projective dimension, Tor-persistent ring, vanishing of Tor",
author = "Olgur Celikbas and Henrik Holm",
year = "2020",
doi = "10.1080/00927872.2020.1756311",
language = "English",
volume = "48",
pages = "4149--4154",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor & Francis",
number = "10",

}

RIS

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