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.
ACKNOWLEDGMENT
Antonio Behn is supported by FONDECYT 1070243. Iván Correa is supported by FONDECYT 1060229. Irvin Roy Hentzel is supported by FONDECYT 7060096 and FIBAS 10-05.
Notes
Communicated by I. P. Shestakov.