On Herstein's Lie map conjectures. I (Q2723474)
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scientific article; zbMATH DE number 1614744
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Herstein's Lie map conjectures. I |
scientific article; zbMATH DE number 1614744 |
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5 July 2001
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Lie maps
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prime algebras
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Lie derivations
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algebras with involutions
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On Herstein's Lie map conjectures. I (English)
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The description of the Lie and Jordan structure of an associative ring \(B\) (or algebra over some unitary commutative ring) is a classical and important problem in ring theory. If \(B\) has an involution \(*\) the skew elements \(K\) under \(*\) form a Lie subalgebra of \(B\). The present paper describes the epimorphisms from Lie ideals of \(B\) onto noncentral Lie ideals of skew elements of a prime algebra \(D\) with involution, under some mild conditions. This answers an open problem of \textit{I. N. Herstein} [Bull. Am. Math. Soc. 67, 517-531 (1961; Zbl 0107.02704)]. Various applications are obtained as well. The proofs of the main results are very nice and elegant. (Also submitted to MR).
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