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http://dx.doi.org/10.4134/BKMS.2009.46.3.599

NOTES ON GENERALIZED DERIVATIONS ON LIE IDEALS IN PRIME RINGS  

Dhara, Basudeb (DEPARTMENT OF MATHEMATICS BELDA COLLEGE)
Filippis, Vincenzo De (DI.S.I.A., FACULTY OF ENGINEERING UNIVERSITY OF MESSINA)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 599-605 More about this Journal
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;
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