Idempotent-prime ideals and Baer-type rings with involution

In this article, we study some idempotent-structures as cP-Baer rings and I-prime rings. Moreover, we define cP-Baer *-rings and I-*-prime *-rings as involutive versions of cP-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 cP-Baer *-rings are given, for instance the polynomial ring R[x] is a cP-Baer *-ring if and only if R is a cP-Baer *-ring.