Semiprimality and nilpotency of nonassociative rings satisfying x(yz)=y(zx)

Abstract

In this article we study nonassociative rings satisfying the polynomial identity x(yz)=y(zx), which we call "cyclic rings." We prove that every semiprime cyclic ring is associative and commutative and that every cyclic right-nilring is solvable. Moreover, we find sufficient conditions for the nilpotency of cyclic right-nilrings and apply these results to obtain sufficient conditions for the nilpotency of cyclic right-nilalgebras. Copyright © Taylor & Francis Group, LLC.