On $U$-Dominant Dimension

Abstract

Let $Λ$ and $Γ$ be artin algebras and $_ΛU_Γ$ a faithfully balanced selforthogonal bimodule. We show that the $U$-dominant dimensions of $_ΛU$ and $U_Γ$ are identical. As applications to the results obtained, we give some characterizations of double dual functors (with respect to $_ΛU_Γ$) preserving monomorphisms and being left exact respectively.