The Auslander-Reiten Conjecture for Group Rings
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Abstract:
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.
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Journal title
volume 17 issue 2
pages 139- 146
publication date 2022-09
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