# GENERALIZED DERIVATIONS WITH ANNIHILATOR CONDITIONS IN PRIME RINGS

• Wang, Yu
• Published : 2011.09.30
• 39 4

#### 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 $au^sH(u)u^t$ = 0 for all u ${\in}$ L, where s; t ${\geq}$ 0 are fixed integers. Then H = 0 unless satisfies $S_4$, the standard identity in four variables.

#### Keywords

prime ring;derivation;generalized derivation;extended centroid;Utumi quotient ring

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