# NOTES ON GENERALIZED DERIVATIONS ON LIE IDEALS IN PRIME RINGS

• Dhara, Basudeb ;
• Filippis, Vincenzo De
• Published : 2009.05.31
• 54 9

#### 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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