Lie Derivations of the Skew Elements of Prime Rings with Involution Original Research Article

LetRbe a prime ring with involution of the first kind, and characteristic ≠2, 3. LetKdenote the skew elements ofR, and letCdenote the extended centroid ofR. Assume that (RC : C)≠1, 4, 16. It is shown that any Lie derivation ofKinto itself can be extended to an ordinary derivation of left angle bracketKright-pointing angle bracket. Counterexamples are given for the low dimension cases.