Generalized derivations with annihilator conditions in prime rings
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 917-922
Printed September 1, 2011
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
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