Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.
GÖLBAŞI, ÖZNUR and KOÇ, EMİNE
"Generalized derivations on Lie ideals in prime rings,"
Turkish Journal of Mathematics: Vol. 35:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss1/3