Isotopy and identities in alternative algebras

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 $f^{(s)}=0$.