A note on skew derivations in prime rings. (Q2902045)
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scientific article; zbMATH DE number 6066753
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on skew derivations in prime rings. |
scientific article; zbMATH DE number 6066753 |
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16 August 2012
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skew derivations
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Lie ideals
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prime rings
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0.95035213
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0.94126904
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A note on skew derivations in prime rings. (English)
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Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\), \(L\) a noncentral Lie ideal of \(R\), and \(D\) a nonzero skew derivation of \(R\). Consider the expression \(P(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)\) for fixed positive integers \(m,n\) and \(r\). The authors prove that if \(P(t)=0\) for all \(t\in L\) then either \(D\) is a derivation or \(R\) satisfies the standard identity \(S_4\) of degree four.
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