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 \(\varph...
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| creator | Macedo Ferreira, Bruno Leonardo Guzzo, Henrique Kaygorodov, Ivan |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2003.03371 |
| format | Article |
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| subjects | Commutators Isomorphism Mapping Mathematics - Rings and Algebras |
| title | Lie maps on alternative rings preserving idempotents |
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