Abstract
Let R be a non-commutative prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, L a non-central Lie ideal of R, G a non-zero generalized derivation of R.
If [G(u), u]n = [G(u), u], for all u ∈ L, with n > 1, then one of the following holds:
(1) R satisfies the standard identity s4(x1, . . . , x4) and there exist a ∈ U and α ∈ C such that G(x) = ax + xa + αx for all x ∈ R;
(2) there exists γ ∈ C such that G(x) = γx for all x ∈ R.
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Mathematical Institute Slovak Academy of Sciences
