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2024 | OriginalPaper | Chapter

On a Functional Identity Involving Power Values of Generalized Skew Derivations on Lie Ideals

Authors : Luisa Carini, Vincenzo De Filippis

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

Let R be a prime ring, $Q_r$ its right Martindale quotient ring and C its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, $m,n,s\ge 1$ positive fixed integers. If

$$ F(u)^n\biggl (F(u)^m-u^m\biggr )^s=0 $$

for all $u\in L$, then there exists $\lambda \in C$ such that $F(x)=\lambda x$, for any $x\in R$, with $\lambda ^m=1$, unless when $char(R)=2$ and $R\subseteq M_2(K)$, the ring of $2\times 2$ matrices over a field K. We will also provide a generalization of the previous result for semiprime rings.

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previous chapter Generalized Derivations with Periodic Values on Prime Rings

next chapter Generalized Skew Derivations with Periodic Values on Lie Ideals

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Title: On a Functional Identity Involving Power Values of Generalized Skew Derivations on Lie Ideals
Authors: Luisa Carini
Vincenzo De Filippis
Publisher: Springer Nature Switzerland
Book: Advances in Ring Theory and Applications
Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50795-3_18

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