Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 49, No. 2, pp. 441-447 (2008)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 441-447 (2008) |
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Strong commutativity preserving maps on Lie ideals of semiprime ringsL. Oukhtite, S. Salhi and L. TaoufiqUniversité Moulay Ismaïl, Faculté des Sciences et Techniques, Département de Mathématiques, Groupe d'Algèbre et Applications, B. P. 509 Boutalamine, Errachidia, Maroc, e-mail: oukhtitel@hotmail.com, e-mail: salhi@fastmail.fm, e-mail: lahcentaoufiq@yahoo.comAbstract: Let $R$ be a $2$-torsion free semiprime ring and $U$ a nonzero square closed Lie ideal of $R$. In this paper it is shown that if $f$ is either an endomorphism or an antihomomorphism of $R$ such that $f(U)=U$, then $f$ is strong commutativity preserving on $U$ if and only if $f$ is centralizing on $U$. Keywords: strong commutativity preserving maps, centralizing maps, semiprime rings, Lie ideals Classification (MSC2000): 16N60, 16U80 Full text of the article:
Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.
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