Semiprimality and Nilpotency of Nonassociative Rings Satisfying x(yz) = y(zx)

Antonio Behn Department of Mathematics, Faculty of Science, University of Chile, Santiago, ChileCorrespondence[email protected]

Iván Correa Department of Mathematics, Metropolitan University Cs. Educación, Santiago, Chile

Irvin Roy Hentzel Department of Mathematics, Iowa State University, Ames, Iowa, USA

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:

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.

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