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arXiv · 2003.03371

Lie maps on alternative rings preserving idempotents

Bruno Leonardo Macedo Ferreira·Henrique Guzzo Jr.·Ivan Kaygorodov
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Abstract

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain assumptions on $\Re$, we prove that $\varphi$ is of the form $\psi + \tau$, where $\psi$ is either an isomorphism or the negative of an anti-isomorphism of $\Re$ onto $\Re'$ and $\tau$ is an additive mapping of $\Re$ into the centre of $\Re'$ which maps commutators into zero.

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Bruno Leonardo Macedo Ferreira, Henrique Guzzo Jr., Ivan Kaygorodov. 2020-03-06. Lie maps on alternative rings preserving idempotents. https://doi.org/10.4064/cm8195-10-2020

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