On automorphisms and commutativity in semiprime rings. (Q2861277)
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scientific article; zbMATH DE number 6225932
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On automorphisms and commutativity in semiprime rings. |
scientific article; zbMATH DE number 6225932 |
Statements
12 November 2013
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automorphisms
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generalized polynomial identities
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semiprime rings
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commutativity theorems
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additive maps
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differential identities
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On automorphisms and commutativity in semiprime rings. (English)
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Let \(\sigma\) be an automorphism of a semiprime ring \(R\). The main result of the paper states that if there exist positive integers \(n_0,n_1,\ldots,n_k\) such that \([[\cdots[\sigma(x^{n_0}),x^{n_1}],x^{n_2}],\cdots],x^{n_k}]=0\) for all \(x\in R\), then \(\sigma(x)-x\) lies in the center of \(R\) for every \(x\in R\).
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