Some Classes of Weakly Prime Center Rings

Let R be a ring. The ring R is called weakly prime center(WPC ring) if ab ∈ Z(R) implies that aRb is an ideal of R. In this paper, we prove that every left(right) duo ring is a WPC ring. Also we introduce some classes of rings with nilpotent Jacobson radical which are WPC rings. Finally, we prove that a simple ring is a WPC ring if and only if it is a domain.