Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie maps on alternative rings preserving idempotents   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.

28
The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an