Generalized Derivations Acting as Lie Homomorphisms on Polynomials in Prime Rings.

Let R be a non-commutative prime ring of characteristic different from 2, with center Z(R) and extrended centroid C and let F be a non-zero generalized derivation of R. Denote by f(R) = {f(r1, . . ., rn) : r1, . . ., rn ∈ R}, the set of all the evaluations of a non-central polynomial f(x1, . . ., xn) over C. If F acts as a Lie homomorphism on f(R) then F is the identity map. [ABSTRACT FROM AUTHOR]