Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 275-282 (2010)

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Commutativity conditions on derivations and Lie ideals in $\sigma$-prime rings

L. Oukhtite, S. Salhi and L. Taoufiq

Université Moulay Ismaïl, Faculté des Sciences et Techniques, Département de Mathématiques, Groupe d'Algèbre et Applications, B. P. 509 Boutalamine, Errachidia, Maroc, e-mail:; e-mail:; e-mail:

Abstract: Let $R$ be a 2-torsion free $\sigma$-prime ring, $U$ a nonzero square closed $\sigma$-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d=0$ or $U\subseteq Z(R)$. 2) If either $d([x,y])=0$ for all $x,y\in U$, or $[d(x),d(y)]=0$ for all $x,y \in U$ and $d$ commutes with $\sigma$ on $U$, then $d=0$ or $U\subseteq Z(R)$.

Keywords: $\sigma$-prime ring, derivation, commutativity

Classification (MSC2000): 16W10, 16W25, 16U80

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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.

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