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Isotopy and identities in alternative algebras


Author: M. Babikov
Journal: Proc. Amer. Math. Soc. 125 (1997), 1571-1575
MSC (1991): Primary 17D05
DOI: https://doi.org/10.1090/S0002-9939-97-03789-1
MathSciNet review: 1376749
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Abstract: In this paper we show how to construct an isomorphism between an alternative algebra $A$ over a field of characteristic $\ne 3$ and its isotope $A^{(1+c)}$, where $c$ is an element of Zhevlakov's radical of $A$. This leads to the equivalence of any polynomial identity $f=0$ in alternative algebras and the isotope identity $f^{(s)}=0$.


References [Enhancements On Off] (What's this?)

  • 1. K. McCrimmon, Homotopes of alternative algebras, Math. Ann. 191 (1971), 253-262. MR 47:1899
  • 2. R. Schafer, Alternative algebras over an arbitrary field, Bull. Amer. Math. Soc. 49 (1943), 549-555. MR 5:33d
  • 3. K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Academic Press, New York and London, 1982. MR 83c:17001

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Additional Information

M. Babikov
Affiliation: Department of Mathematics Ohio State University Columbus, Ohio 43202
Email: brkvch@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03789-1
Received by editor(s): March 28, 1995
Communicated by: Lance W. Small
Article copyright: © Copyright 1997 American Mathematical Society

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