Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 51, No. 2, pp. 345-351 (2010)
|
|
Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 2, pp. 345-351 (2010) |
|
|
Generalized derivations and commutativity of rings with involutionL. 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: salhisalh@gmail.com e-mail: lahcentaoufiq@gmail.comAbstract: Let $(R,\star)$ be a $2$ -torsion free ring with involution and $ F$ a generalized derivation, associated to a derivation $d$, satisfying one of the following conditions: 1) for each $x,y\in R$ either $d(x)\circ F(y)=0$ or $d(x)\circ F(y)=x\circ y$. 2) for each $x,y\in R$ either $[d(x),F(y)]=0$ or $[d(x),F(y)]= [x,y]$. In this paper it is shown that if $R$ is $\star$-prime, then $R$ is a commutative ring. Moreover, examples proving the necessity of the $\star$-primeness condition are given. Keywords: rings with involution, generalized derivation, commutativity Classification (MSC2000): 16W10, 16W25, 16N60 Full text of the article (for subscribers):
Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.
© 2010 Heldermann Verlag
|