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Article
Experimenting with the Identity (xy)z = y(zx)
Journal of Symbolic Computation
  • Irvin Roy Hentzel, Iowa State University
  • David P. Jacobs, Clemson University
  • Sekhar V. Muddana, Clemson University
Document Type
Article
Disciplines
Publication Version
Accepted Manuscript
Publication Date
9-1-1993
DOI
10.1006/jsco.1993.1047
Abstract

An experiment with the nonassociative algebra program Albert led to the discovery of the following surprising theorem. Let G be a groupoid satisfying the identity (xy)z = y(zx). Then for products in G involving at least five elements, all factors commute and associate. A corollary is that any semiprime ring satisfying this identity must be commutative and associative, generalizing a known result of Chen.

Comments

This article is published as Hentzel, Irvin Roy, David P. Jacobs, and Sekhar V. Muddana. "Experimenting with the identity (xy) z= y (zx)." Journal of symbolic computation 16, no. 3 (1993): 289-293. 10.1006/jsco.1993.1047. Posted with permission.

Creative Commons License
Creative Commons Attribution-Noncommercial-No Derivative Works 4.0
Copyright Owner
Academic Press
Language
en
File Format
application/pdf
Citation Information
Irvin Roy Hentzel, David P. Jacobs and Sekhar V. Muddana. "Experimenting with the Identity (xy)z = y(zx)" Journal of Symbolic Computation Vol. 16 Iss. 3 (1993) p. 289 - 293
Available at: http://works.bepress.com/irvin-hentzel/32/