On right McCoy rings and right McCoy rings relative to u.p.-monoids

Abstract

In this paper, we prove that all right duo rings are right McCoy relative to any u.p.-monoid. We also show that for any nontrivial u.p.-monoid M, the class of right McCoy rings relative to M is contained in the class of right McCoy rings, and we present an example of a u.p.-monoid M for which this containment is strict.