Notes on generalized derivations on Lie ideals in prime rings
Bull. Korean Math. Soc. 2009 Vol. 46, No. 3, 599-605
https://doi.org/10.4134/BKMS.2009.46.3.599
Printed May 1, 2009
Basudeb Dhara and Vincenzo De Filippis
Belda College and University of Messin
Abstract : Let $R$ be a prime ring, $H$ a generalized derivation of $R$ and $L$ a noncommutative Lie ideal of $R$. Suppose that $u^sH(u)u^t=0$ for all $u \in L$, where $s\geq 0, t\geq 0$ are fixed integers. Then $H(x)=0$ for all $x\in R$ unless char$R=2$ and $R$ 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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