Vol. 60, No. 2, 1975

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ISSN: 0030-8730
Generalized right alternative rings

Irvin Roy Hentzel

Vol. 60 (1975), No. 2, 95–102
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
Authors
Irvin Roy Hentzel