Commutativity of Involutorial Rings with Constraints on Left Multipliers

L. Oukhtite, L. Taoufiq

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.

Keywords


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

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DOI: http://dx.doi.org/10.26713%2Fcma.v2i1.128

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eISSN 0975-8607; pISSN 0976-5905