Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Isotopy and identities in alternative algebras

Author(s): M. Babikov
Journal: Proc. Amer. Math. Soc. 125 (1997), 1571-1575.
MSC (1991): Primary 17D05
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:

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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