Generalized derivations as homomorphisms or anti-homomorphisms on Lie ideals

Let RR be a prime ring of char(R)≠2char(R)≠2, ZZ the center of RR, and LL a nonzero Lie ideal of RR. If RR admits a generalized derivation FF associated with a derivation dd which acts as a homomorphism or as anti-homomorphism on LL, then either d=0d=0 or L⊆ZL⊆Z. This result generalizes a theorem of Wang and You.