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Annihilators and Power Values of Generalized Skew Derivations on Lie Ideals

Published online by Cambridge University Press:  20 November 2018

Vincenzo De Filippis
Vincenzo De Filippis*
Affiliation:
Department of Mathematics and Computer Science, University of Messina, 98166, Messina, Italy e-mail: defilippis@unime.it
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Abstract

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Let $R$ be a prime ring of characteristic diòerent from $2$, let ${{Q}_{r}}$ be its right Martindale quotient ring, and let $C$ be its extended centroid. Suppose that $F$ is a generalized skew derivation of $R,\,L$ a non-central Lie ideal of $R,\,0\,\ne \,a\,\in \,R,\,m\,\ge \,0$ and $n,\,s\,\ge \,1$ fixed integers. If

$$a{{\left( {{u}^{m}}F\left( u \right){{u}^{n}} \right)}^{s}}\,=\,0$$

for all $u\,\in \,L$, then either $R\,\subseteq \,{{M}_{2}}\left( C \right)$, the ring of $2\,\times \,2$ matrices over $C$, or $m\,=\,0$ and there exists $b\,\in \,{{Q}_{r}}$ such that $F\left( x \right)\,=\,bx$, for any $x\,\in \,R$, with $ab\,=\,0$.

Keywords

16W2516N60generalized skew derivationprime ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 2 , 01 June 2016 , pp. 258 - 270
Copyright
Copyright © Canadian Mathematical Society 2016

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