Dependent elements of derivations on semiprime rings. (Q1028882)
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scientific article; zbMATH DE number 5576473
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dependent elements of derivations on semiprime rings. |
scientific article; zbMATH DE number 5576473 |
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Dependent elements of derivations on semiprime rings. (English)
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9 July 2009
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Summary: We characterize dependent elements of a commuting derivation \(d\) on a semiprime ring \(R\) and investigate a decomposition of \(R\) using dependent elements of \(d\). We show that there exist ideals \(U\) and \(V\) of \(R\) such that \(U\oplus V\) is an essential ideal of \(R\), \(U\cap V=\{0\}\), \(d=0\) on \(U\), \(d(V)\subseteq V\), and \(d\) acts freely on \(V\).
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dependent elements
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commuting derivations
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semiprime rings
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