The socle of the last term in a minimal injective resolution

Abstract

Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k − 2)-Gorenstein with the injective dimensions of Λ U and U Γ being k, then the socle of the last term in a minimal injective resolution of Λ U is non-zero.