On an extension of a result of Herstein. (Q2847698)
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scientific article; zbMATH DE number 6207509
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an extension of a result of Herstein. |
scientific article; zbMATH DE number 6207509 |
Statements
11 September 2013
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prime rings
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semiprime rings
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derivations
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center
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On an extension of a result of Herstein. (English)
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Let \(R\) be a \(2\)-torsion free ring with a derivation \(T\colon R\to R\) such that \([T(R),T(R)]=0\). The authors show that if \(I\) is the ideal of \(R\) generated by \(T(R)\), then \(I^3\) lies in the center of \(R\). Moreover, they show that \(R\) has an ideal \(K\) contained in the kernel of \(T\), \(K^2=0\), and \([T(R/K),R/K]\) generates a trivial ideal of \(R/K\).
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