Підтримка:The second named author was partially supported by Conselho Nacional de De-senvolvimento Cientfico e Tecnolgico (CNPq, Brazil) and the third named author waspartially supported by Capes (Brazil)
In this paper we consider rings R with a partial action α of 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.