Idempotent-prime ideals and Baer-type rings with involution

Abstract

In this article, we study some idempotent-structures as c P -Baer rings and I -prime rings. Moreover, we define c P -Baer *-rings and I -*-prime *-rings as involutive versions of c P -Baer rings and I -prime rings and expose their properties. Furthermore, the relation between these rings and those without involution are indicated. Finally, some extensions for c P -Baer *-rings are given, for instance the polynomial ring R [ x ] is a c P -Baer *-ring if and only if R is a c P -Baer *-ring.