TY - JOUR
AU - Hermas, A.
AU - Oukhtite, L.
AU - Taoufiq, L.
PY - 2023/09/22
Y2 - 2024/02/24
TI - Generalized derivations acting on Lie ideals in prime rings and Banach algebras
JF - Matematychni Studii
JA - Mat. Stud.
VL - 60
IS - 1
SE - Articles
DO - 10.30970/ms.60.1.3-11
UR - http://www.matstud.org.ua/ojs/index.php/matstud/article/view/394
SP - 3-11
AB - 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.
ER -