Commutativity of Involutorial Rings with Constraints on Left Multipliers

L. Oukhtite; L. Taoufiq

doi:10.26713/cma.v2i1.128

Authors

L. Oukhtite Université Moulay Ismaí¯l, Faculté des Sciences et Techniques, Déepartement de Mathématiques, Groupe d'Algèebre et Applications, B.P. 509 Boutalamine, Errachidia;
L. Taoufiq Université Moulay Ismaí¯l, Faculté des Sciences et Techniques, Déepartement de Mathématiques, Groupe d'Algèebre et Applications, B.P. 509 Boutalamine, Errachidia;

DOI:

https://doi.org/10.26713/cma.v2i1.128

Keywords:

Rings with involution, $\ast$-prime rings, Generalized derivations, Commutativity

Abstract

Let $(R, \ast)$ be a ring with involution and let $Z(R)$ be the center of $R$. The purpose of this paper is to explore the commutativity of $R$ if it admits a left multiplier $F$ satisfying certain identities on Lie ideals. Furthermore, some results for left multipliers in prime rings are extended to Lie ideals. Finally, examples are given to prove that the restrictions imposed on the hypothesis of the various theorems were not superfluous.

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