Volume 17, Issue 2 (9-2022)                   IJMSI 2022, 17(2): 139-146 | Back to browse issues page

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Bahlekeh A. The Auslander-Reiten Conjecture for Group Rings. IJMSI 2022; 17 (2) :139-146
URL: http://ijmsi.ir/article-1-1428-en.html
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga$ is a finite acyclic group.
Type of Study: Research paper | Subject: Special

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