A result on generalized skew derivations on Lie ideals in prime rings

摘要

Let R be a prime ring of characteristic different from 2, C its extended centroid, L a noncentral Lie ideal of R and m, n, t ≥ 1 fixed integers. Suppose that F is a nonzero generalized skew derivation of R such that u~m F(u)~tu~n = 0, for all u ∈ L. Then dimC RC = 4.