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# Annihilators and Power Values of Generalized Skew Derivations on Lie Ideals

Published:2016-02-03
Printed: Jun 2016
• Vincenzo De Filippis,
Department of Mathematics and Computer Science, University of Messina, 98166, Messina, Italy
 Format: LaTeX MathJax PDF

## Abstract

Let $R$ be a prime ring of characteristic different from $2$, $Q_r$ be its right Martindale quotient ring and $C$ be its extended centroid. Suppose that $F$ is a generalized skew derivation of $R$, $L$ a non-central Lie ideal of $R$, $0 \neq a\in R$, $m\geq 0$ and $n,s\geq 1$ fixed integers. If $a\biggl(u^mF(u)u^n\biggr)^s=0$ for all $u\in L$, then either $R\subseteq M_2(C)$, the ring of $2\times 2$ matrices over $C$, or $m=0$ and there exists $b\in Q_r$ such that $F(x)=bx$, for any $x\in R$, with $ab=0$.
 Keywords: generalized skew derivation, prime ring
 MSC Classifications: 16W25 - Derivations, actions of Lie algebras 16N60 - Prime and semiprime rings [See also 16D60, 16U10]

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