On U-codominant dimension

Abstract

Let R and S be semiregular rings and U a semidualizing $(R,S)$-bimodule. We show that the U-codominant dimensions of ${}_{R}U$ and $U_S$ are identical. As an application, we get that the U-codominant dimension of U is at least two if and only if the functor $U{\otimes }_S{Hom}_R(U,-)$ is right exact and if and only if the functor ${Hom}_R(U,U{\otimes }_S-)$ is left exact. We also get some new equivalent characterizations of (n-)Auslander algebras.