Transactions of the American Mathematical Society

Author(s): K. I. Beidar; M. Bresar; M. A. Chebotar; W. S. Martindale III
Journal: Trans. Amer. Math. Soc. 353 (2001), 4235-4260.
MSC (1991): Primary 16W10, 16W20, 16R50
Posted: June 6, 2001
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We describe surjective Lie homomorphisms from Lie ideals of skew elements of algebras with involution onto noncentral Lie ideals (factored by their centers) of skew elements of prime algebras ${\mathcal{D}}$ with involution, provided that $\operatorname{char}({\mathcal{D}})\not=2$ and ${\mathcal{D}}$ is not PI of low degree. This solves the last remaining open problem of Herstein on Lie isomorphisms module cases of PI rings of low degree. A more general problem on maps preserving any polynomial is also discussed.

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K. I. Beidar
Affiliation: Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan
Email: beidar@mail.ncku.edu.tw

M. Bresar
Affiliation: Department of Mathematics, PF, University of Maribor, Maribor, Slovenia
Email: bresar@uni-mb.si

M. A. Chebotar
Affiliation: Department of Mechanics and Mathematics, Tula State University, Tula, Russia
Email: mchebotar@tula.net

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