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

Q3 Mathematics
A. Hermas, L. Oukhtite, L. Taoufiq
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引用次数: 0

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.
作用于素环和巴拿赫代数中李理想的广义导数
设$R$是一个素环,$L$是$R的非中心李理想。本文的目的是描述$R$在$L上局部满足某些代数恒等式的广义导数。更确切地说,我们考虑素环R的两个广义导数F_1和F_2满足下列恒等式之一:$F_1(x)\circ y +x \circ F_2(y) =0,$2。美元(f (x), y] +₂((x, y)) = 0, x, y美元对所有美元在一个偏心的谎言理想L R美元美元。进一步,作为一个应用,我们研究了一类素数Banach代数的非空开子集上具有幂值的满足相似代数恒等式的连续广义导数。我们的拓扑方法是基于贝尔范畴定理和泛函分析的一些性质。
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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