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.

Key Words:

• Nonassociative semiprime nilpotent identity algebra

2000 Mathematics Subject Classification:

• 17A30
• 16N60

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.