Title: Lie Derivations on Skew Elements in Prime Rings With Involution
Abstract: Abstract Let R be a prime ring with involution satisfying x/2 ∊ R whenever x ∊ R . Assume that R has two nontrivial symmetric idempotents e 1 , e 2 whose sum is not 1, and that the subrings determined by e 1 , e 2 , 1 — (e 1 + e 2 ) are not orders in simple rings of dimension at most 4 over their centers. Then if L is a Lie derivation of the skew elements K into R there exists a subring A of R , A ⊆ , a derivation D : A → RC , the central closure of R, and a mapping T : R → C , satisfying L = D + T on K and = 0.