Generalized right alternative rings

Irvin Roy Hentzel

Vol. 60 (1975), No. 2, 95–102

DOI: 10.2140/pjm.1975.60.95

Abstract

We show that weakening the hypotheses of right alternative rings to the three identities

1. (ab,c,d) + (a,b,[c,d]) = a(b,c,d) + (a,c,d)b
2. (a,a,a) = 0
3. ([a,b],b,b) = 0

for all a, b, c, d in the ring will not lead to any new simple rings. In fact, the ideal generated by each associator of the form (a,b,b) is a nilpotent ideal of index at most three. Our proofs require characteristic ≠2, ≠3.

Mathematical Subject Classification 2000

Primary: 17A30

Milestones

Received: 17 May 1974

Published: 1 October 1975