Generalized derivations in prime rings and noncommutative Banach algebras
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 621-629
Printed December 1, 2008
Vincenzo De Filippis
University of Messina
Abstract : Let $R$ be a prime ring of characteristic different from $2$, $C$ the extended centroid of $R$, and $\delta$ a generalized derivations of $R$. If $[[\delta(x),x],\delta(x)]=0$ for all $x\in R$ then either $R$ is commutative or $\delta(x)=ax$ for all $x\in R$ and some $a \in C$. We also obtain some related result in case $R$ is a Banach algebra and $\delta$ is either continuous or spectrally bounded.
Keywords : prime ring, derivations, differential identities, Banach algebras
MSC numbers : Primary 16N60; Secondary 16W25
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail:   | Powered by INFOrang Co., Ltd