ON THE VANISHING OF SELF EXTENSIONS OVER COHEN-MACAULAY LOCAL RINGS

被引：3
|
作者：
Araya, Tokuji [1 ]
Celikbas, Olgur [2 ]
Sadeghi, Arash [3 ]
Takahashi, Ryo [4 ]
机构：
[1] Okayama Univ Sci, Fac Sci, Dept Appl Sci, Kita Ku, Okayama 7000005, Japan
[2] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA
[3] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran
[4] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 11期
关键词：
Auslander-Reiten Conjecture; vanishing of Ext and Tor; canonical modules; AUSLANDER-REITEN CONJECTURE; COHOMOLOGY; MODULES;
D O I：
10.1090/proc/13944
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：4563 / 4570
页数：8
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