Auslander-Reiten conjecture and finite injective dimension of Hom
Abstract
For a finitely generated module M over a commutative Noetherian ring R, we settle the Auslander-Reiten conjecture when at least one of HomR(M,R) and HomR(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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