Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(5): 917-922

Printed September 1, 2011

https://doi.org/10.4134/BKMS.2011.48.5.917

Copyright © The Korean Mathematical Society.

Generalized derivations with annihilator conditions in prime rings

Yu Wang

Shanghai Normal University

Abstract

Let $R$ be a prime ring, $H$ a generalized derivation of $R$, $L$ a noncentral Lie ideal of $R$, and $0\neq a\in R$. Suppose that $au^{s}H(u)u^{t}=0$ for all $u\in L$, where $s,t\geq 0$ are fixed integers. Then $H=0$ unless $R$ satisfies $S_{4}$, the standard identity in four variables.

Keywords: prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring

MSC numbers: 16W25, 16N60, 16R50