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arXiv · 2109.00692

Auslander-Reiten conjecture and finite injective dimension of Hom

Dipankar Ghosh·Ryo Takahashi
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Abstract

For a finitely generated module $ M $ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\rm Hom}_R(M,R)$ and ${\rm Hom}_R(M,M)$ has finite injective dimension. A number of new characterizations of Gorenstein local rings are also obtained in terms of vanishing of certain Ext and finite injective dimension of Hom.

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Dipankar Ghosh, Ryo Takahashi. 2021-09-02. Auslander-Reiten conjecture and finite injective dimension of Hom. https://doi.org/10.1215/21562261-2023-0016

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