Jacobson investigated the structure of rings with the property that some power of each element is central, in the procedure of the study of commutativity. In this paper, we consider a class of rings in which this property occurs only for central elements, and such rings are called ppnc. We first prove that a noncommutative ppnc ring is infinite, and that a ppnc ring is commutative when it is a K-ring or a locally finite ring. We next study the structure of ppnc rings, and the relation between ppnc rings and related concepts (for example, K-rings, commutative rings and NI rings), through matrix rings, polynomial rings, right quotient rings and direct products.
