Annihilators of power central values of generalized Skew derivations on Lie ideals. (English) Zbl 07880376
Summary: Let \(R\) be a prime ring with center \(Z(R)\) and \(G\) be a generalized \(\alpha \)-derivation of \(R\) for \(\alpha \in\operatorname{Aut} (R)\). Let \(a\in R\) be a nonzero element and \(n\) be a fixed positive integer.
- (i)
- If \(aG(x)^n \in Z(R)\) for all \(x \in R\) then \(aG(x) = 0\) for all \(x \in R\) unless \(\dim_C RC = 4\).
- (ii)
- If \(aG(x)^n \in Z(R)\) for all \(x \in L\), where \(L\) is a noncommutative Lie ideal of \(R\) then \(aG(x) = 0\) for all \(x \in R\) unless \(\dim_C RC = 4\).
MSC:
| 16W20 | Automorphisms and endomorphisms |
| 16W25 | Derivations, actions of Lie algebras |
| 16N60 | Prime and semiprime associative rings |
Keywords:
prime ring; Lie ideal; generalized skew derivation; generalized derivation; automorphism; right Martindale quotient ring; two-sided Martindale quotient ring; generalized polynomial identityReferences:
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| [32] | DOI: 10.61186/ijmsi.19.1.35 ] [ Downloaded from ijmsi.ir on 2024-05-28 ] Powered by TCPDF (www.tcpdf.org) · Zbl 07880376 · doi:10.61186/ijmsi.19.1.35 |
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