On $U$-Dominant Dimension

Abstract

Let $\Lambda$ and $\Gamma$ be artin algebras and ${}_{\Lambda }{U}_{\Gamma }$ a faithfully balanced selforthogonal bimodule. We show that the $U$-dominant dimensions of ${}_{\Lambda }U$ and $U_{\Gamma }$ are identical. As applications to the results obtained, we give some characterizations of double dual functors (with respect to ${}_{\Lambda }{U}_{\Gamma }$) preserving monomorphisms and being left exact respectively.

13 pages