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On Prime Right Alternative Algebras and Alternators
Mathematical Reports of the Academy of Sciences – Comptes Rendus Mathématiques
  • Giulia Maria Piacentini Cattaneo, Italian National Research Council
  • Irvin R. Hentzel, Iowa State University
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
2-1-1984
Abstract

We study subvarieties of the variety of right alternative algebras over a field of characteristic t2,t3 such that the defining identities of the variety force the span of the alternators to be an ideal and do not force an algebra with identity element to be alternative. We call a member of such a variety a right alternative alternator ideal algebra. We characterize the algebras of this subvariety by finding an identity which holds if and only if an algebra belongs to the subvariety. We use this identity to prove that if R is a prime, right alternative alternator ideal algebra with an idempotent e to,tl such that (e,e,R) =O, then either R is alternative or R belongs to one of four exceptional varieties.

Comments

This article is published as Hentzel, Irvin Roy and Giulia Maria Piacentini Cattaneo “On Prime Right Alternative Algebras and Alternators,” Mathematical Reports – Comptes rendus mathématiques, v. 6, no.1 (1984): 3-8.

Copyright Owner
Royal Society of Canada
Language
en
File Format
application/pdf
Citation Information
Giulia Maria Piacentini Cattaneo and Irvin R. Hentzel. "On Prime Right Alternative Algebras and Alternators" Mathematical Reports of the Academy of Sciences – Comptes Rendus Mathématiques Vol. 6 Iss. 1 (1984) p. 3 - 8
Available at: http://works.bepress.com/irvin-hentzel/26/