Certain functional identities involving a pair of generalized skew derivations with nilpotent values on Lie ideals.

Let R be a prime ring of characteristic different from 2, Q_r its right Martindale quotient ring, L a non-central Lie ideal of R (i.e., L , R ≠ 0 ), n ≥ 1 a fixed integer, F and G two generalized skew derivations of R, associated with the same automorphism α of R. If (F (x y) − G (x) y) n = 0 , for any x , y ∈ L , then there exists a ∈ Q r such that , for any x ∈ R , unless when R satisfies the standard polynomial identity s 4 (x 1 , ... , x 4) . [ABSTRACT FROM AUTHOR]