Cocentralizing Derivations And Nilpotent Values On Lie Ideals

Let R be a prime ring with charR ±= 2, L a non-central Lie ideal of R, d, g non-zero derivations of R, n?1 a fixed integer. We prove that if (d(x)x - xg(x))n = 0 for all x?L, then either d = g = 0 or R satisfies the standard identity s4 and d,g are inner derivations, induced respectively by the elements a and b such that a + b?Z(R). © Indian National Science Academy.