A result concerning nilpotent values with generalized skew derivations on Lie ideals

摘要

Let n >= 1 be a fixed integer, R a prime ring with its right Martindale quotient ring Q, C the extended centroid, and L a non-central Lie ideal of R. If F is a generalized skew derivation of R such that (F(x)F(y)-yx)(n) = 0 for all x,y is an element of L, then char(R) = 2 and R subset of M-2(C), the ring of 2x2 matrices over C.