Gorenstein injective modules and Auslander categories

摘要

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an R-module M, we show that M is Gorenstein injective if and only if Hom R (?,M) belongs to Auslander category B(?), M is cotorsion and Ext i R (E,M) = 0 for all injective R-modules E and all i > 0.