COMMUTATIVITY OF π-STRONGLY PERIODIC RINGS

Assume that R is a ring, with the set N of nilpotent elements, Jacobson radical J, and center Z. In this paper, R is called pi-strongly periodic if there exist positive integers m, n of opposite parity for each x is an element of R\(J boolean OR N) such that x(n) - x(m) is an element of (J vertical bar I N). We prove some results about the commutativity of it pi-S-P rings.