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On the vanishing of self extensions over Cohen-Macaulay local rings

2017/03/17 by Tokuji Araya, Araya, Tokuji, Olgur Celikbas +5
Mathematics · #13D07 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13D07 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1703.06160

6 pages

arxiv created 2017/03/17 · openalex publication_date 2017/03/17 · arxiv updated 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a module, is one of the long-standing 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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