Isotopy and identities in alternative algebras
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- by M. Babikov PDF
- Proc. Amer. Math. Soc. 125 (1997), 1571-1575 Request permission
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
- Kevin McCrimmon, Homotopes of alternative algebras, Math. Ann. 191 (1971), 253–262. MR 313344, DOI 10.1007/BF01350327
- Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
- Susumu Okubo and J. Marshall Osborn, Algebras with nondegenerate associative symmetric bilinear forms permitting composition. II, Comm. Algebra 9 (1981), no. 20, 2015–2073. MR 640611, DOI 10.1080/00927878108822695
Additional Information
- M. Babikov
- Affiliation: Department of Mathematics Ohio State University Columbus, Ohio 43202
- Email: brkvch@math.ohio-state.edu
- Received by editor(s): March 28, 1995
- Communicated by: Lance W. Small
- © Copyright 1997 American Mathematical Society
- 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