Notes on Lie ideals of simple Artinian rings. (Q2853974)
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scientific article; zbMATH DE number 6215933
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Notes on Lie ideals of simple Artinian rings. |
scientific article; zbMATH DE number 6215933 |
Statements
17 October 2013
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simple rings
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simple Artinian rings
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division rings
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Lie ideals
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Lie rings
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Notes on Lie ideals of simple Artinian rings. (English)
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Let \(R\) be a simple Artinian ring. Herstein proved that when the characteristic of \(R\) is not 2, then (1) any Lie ideal of \(R\) is central or contains the commutator subgroup \([R,R]\), and (2) \([R,R]/Z([R,R])\) is simple as a Lie algebra. In this article the authors extend these two results to all characteristics when the matrix size of \(R\) is at least 3. Their proofs are elementary and algebraic.
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