Generalized derivations acting on Lie ideals in prime rings and Banach algebras

A. Hermas; L. Oukhtite; L. Taoufiq

doi:10.30970/ms.60.1.3-11

A. Hermas Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University Fez, Morocco
L. Oukhtite University Sidi Mohamed Ben Abdella, Fès
L. Taoufiq National School of Applied Sciences, Ibn Zohr University Agadir, Morocco

DOI: https://doi.org/10.30970/ms.60.1.3-11

Анотація

Let $R$ be a prime ring and $L$ a non-central Lie ideal of $R.$ The purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities locally on $L.$ More precisely, we consider two generalized derivations $F_1$ and $F_2$ of a prime ring $R$ satisfying one of the following identities:
1. $F_1(x)\circ y +x \circ F_2(y) =0,$
2. $[F_1(x),y] + F_2([x,y]) =0,$
for all $x,y$ in a non-central Lie ideal $L$ of $R.$ Furthermore, as an application, we study continuous generalized derivations satisfying similar algebraic identities with power values on nonvoid
open subsets of a prime Banach algebra $A$. Our topological approach is based on Baire's
category theorem and some properties from functional analysis.

Біографії авторів

A. Hermas, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University Fez, Morocco

Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University
Fez, Morocco

L. Oukhtite, University Sidi Mohamed Ben Abdella, Fès

Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University
Fez, Morocco

L. Taoufiq, National School of Applied Sciences, Ibn Zohr University Agadir, Morocco

National School of Applied Sciences, Ibn Zohr University
Agadir, Morocco

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