Auslander-Reiten Sequences for Gorenstein Rings of Dimension One

被引：0
|
作者：
Roy, Robert [1 ]
机构：
[1] 215 Carnegie Bldg, Syracuse, NY 13244 USA
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2019年 / 22卷 / 04期
基金：
美国国家科学基金会;
关键词：
Commutative algebra; Auslander-reiten theory; Gorenstein;
D O I：
10.1007/s10468-018-9805-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let R be a complete local Gorenstein ring of dimension one, with maximal ideal ?. We show that if M is a Cohen-Macaulay R-module which begins an AR-sequence, then this sequence is produced by a particular endomorphism of ? corresponding to a minimal prime ideal of R. We apply this result to determining the shape of some components of stable Auslander-Reiten quivers, which in the considered examples are shown to be tubes.
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页码：909 / 935
页数：27
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