Author:
Hermas A.,Oukhtite L.,Taoufiq L.
Abstract
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 nonvoidopen subsets of a prime Banach algebra $A$. Our topological approach is based on Baire'scategory theorem and some properties from functional analysis.
Publisher
Ivan Franko National University of Lviv
Reference20 articles.
1. M. Ashraf, B.A. Wani, On commutativity of rings and Banach algebras with generalized derivations, Adv. Pure. Appl. Math., 10 (2019), no.2, 155–163.
2. M. Ashraf, N. Rehman, M. Rahman, On generalized derivations and commutativity of rings, Int. J. Math. Game Theory Algebra, 18 (2009), no.2, 81–86.
3. J. Bergen, I.N. Herstein, J.W. Keer, Lie ideals and derivations of prime rings, J. Algebra, 71 (1981), no.1, 259–267.
4. F.F. Bonsall, J. Duncan, Complete normed algebras, Springer-Verlag, New York, 1973.
5. K. Bouchannafa, M.A. Idrissi, L. Oukhtite, Relationship between the structure of a quotient ring and the behavior of certain additive mappings, Comm. Korean Math. Soc., 37 (2022), no.2, 359–370.
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