Auslander-Reiten conjecture and finite injective dimension of Hom

Dipankar Ghosh, Ryo Takahashi

For a finitely generated module $M$ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\mathrm{Hom}}_R(M,R)$ and ${\rm Hom}_R(M,M…