Product of generalized skew derivations on Lie ideals

摘要

Let R be a non-commutative prime ring of characteristic different from 2, Q(r) be its right Martindale quotient ring and C be its extended centroid and L be a non-central Lie ideal of R Let F and G be two non-zero generalized skew derivations of R, associated with the same automorphism alpha and commuting with alpha. If F(G(x)x) = 0 for all x is an element of L, then one of the following holds: