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

Lie maps on alternative rings preserving idempotents