Quasi-duo Partial skew polynomial rings

Abstract

In this paper we consider rings \(R\) with a partial action \(\alpha\) of \(\mathbb{Z}\) on \(R\). We give necessary and sufficient conditions for partial skew polynomial rings and partial skew Laurent polynomial rings to be quasi-duo rings and in this case we describe the Jacobson radical. Moreover, we give some examples to show that our results are not an easy generalization of the global case.