On quasi-duo differential polynomial rings

Abstract

In this paper, we prove a necessary and sufficient condition on a ring [Formula: see text] with a derivation [Formula: see text] for the differential polynomial ring [Formula: see text] to be right quasi-duo. More precisely, [Formula: see text] is right quasi-duo if and only if [Formula: see text] is commutative and [Formula: see text] where [Formula: see text] is the intersection of [Formula: see text] with the Jacobson radical of [Formula: see text]. The proof is simple and corrects the original proof by Bien and Oinert.