On the vanishing of self extensions over Cohen-Macaulay local rings
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- by Tokuji Araya, Olgur Celikbas, Arash Sadeghi and Ryo Takahashi PDF
- Proc. Amer. Math. Soc. 146 (2018), 4563-4570 Request permission
Abstract:
The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a module, is one of the longstanding conjectures in ring theory. Although it is still open, there are several results in the literature that establish the conjecture over Gorenstein rings under certain conditions. The purpose of this article is to obtain extensions of such results over Cohen-Macaulay local rings that admit canonical modules. In particular, our main result recovers theorems of Araya, and Ono and Yoshino simultaneously.References
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Additional Information
- Tokuji Araya
- Affiliation: Department of Applied Science, Faculty of Science, Okayama University of Science, Ridaicho, Kitaku, Okayama 700-0005, Japan
- MR Author ID: 639398
- Email: araya@das.ous.ac.jp
- Olgur Celikbas
- Affiliation: Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310
- MR Author ID: 942955
- ORCID: 0000-0002-5306-7589
- Email: olgur.celikbas@math.wvu.edu
- Arash Sadeghi
- Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
- MR Author ID: 937081
- ORCID: 0000-0002-6856-3243
- Email: sadeghiarash61@gmail.com
- Ryo Takahashi
- Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
- MR Author ID: 674867
- Email: takahashi@math.nagoya-u.ac.jp
- Received by editor(s): March 17, 2017
- Received by editor(s) in revised form: June 8, 2017
- Published electronically: August 7, 2018
- Additional Notes: The first and fourth authors were partly supported by JSPS Grants-in-Aid for Scientific Research 26400056 and 16K05098, respectively. The third author’s research was supported by a grant from IPM
- Communicated by: Jerzy Weyman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4563-4570
- MSC (2010): Primary 13D07, 13H10
- DOI: https://doi.org/10.1090/proc/13944
- MathSciNet review: 3856128