论文标题
躺在替代戒指上保存dipottents
Lie maps on alternative rings preserving idempotents
论文作者
论文摘要
令$ \ re $和$ \ re'$ unital $ 2 $，$ 3 $ torsion免费替代环和$φ：\ re \ rightarrow \ re'$是保留iDempotents的溢流式乘法。假设$ \ re $具有非平凡的依据。根据$ \ re $的某些假设，我们证明$φ$是$ψ+τ$的形式，其中$ψ$是同构的，或者是$ \ re $ $ \ re $ $ \ re \ re'$和$τ$的抗异态性的否定，是$ \ re $ \ re $ \ re \ re pe re'$ \ re \ re're're're retorator的$ \ re $ $ \ re \ re'的添加映射。
Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $φ: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain assumptions on $\Re$, we prove that $φ$ is of the form $ψ+ τ$, where $ψ$ is either an isomorphism or the negative of an anti-isomorphism of $\Re$ onto $\Re'$ and $τ$ is an additive mapping of $\Re$ into the centre of $\Re'$ which maps commutators into zero.
