文摘
Let R be a prime ring with its Utumi ring of quotients U and extended centroid C. Suppose that F is a generalized derivation of R and L is a noncentral Lie ideal of R such that F(u)[F(u), u] n = 0 for all u ?L, where n ?1 is a fixed integer. Then one of the following holds: (1) there exists λ ?C such that F(x) = λx for all x ?R