On Lie ideals with derivations as homomorphisms and anti-homomorphisms.

In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u2 ε U, for all u ε U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ⫅ Z(R). [ABSTRACT FROM AUTHOR]