Dualizing Modules for Orders and Artin Algebras

We provide a criterion for a Λ-bimodule ω to be a dualizing module, where Λ is an order over a commutative Gorenstein complete local domain of dim R=1. Using this criterion, we give examples of dualizing modules which are neither isomorphic to Λ nor a dual of Λ. Thus we can also give such examples over an Artin algebra by modulo a nonzerodivisor.