Generalized Skew-Derivations on Lie Ideals in Prime Rings

摘要

Let R be a prime ring with characteristic different from 2, Q_r be its right Martindale quotient ring, C be its extended centroid, F a nonzero generalized skew derivation of R, La noncentral Lie ideal of R, n ≥ 1, m ≥ 0 be fixed integers and 0 ≠ a ∈ R. If au~mF(u)~n = 0 for all u ∈ L, then one of the following holds: (i) m = 0 and there exists b ∈ Q_r such that F(x) = bx for all x ∈ R with ab = 0; (ii) R satisfies S4.