Aydin, NesetTurkmen, Selin2025-01-272025-01-2720171225-17632234-3024https://doi.org/10.4134/CKMS.c170019https://hdl.handle.net/20.500.12428/28781In this paper, we define a set including of all f(a) with a is an element of R generalized derivations of R and is denoted by f(R). It is proved that (i) the mapping g : L (R) -> f(R) given by g (a) = f(-a) for all a is an element of R is a Lie epimorphism with kernel N-sigma,N-tau; (ii) if R is a semiprime ring and sigma is an epimorphism of R, the mapping h : f(R) -> I (R) given by h(f(a)) = i(sigma)(-a) is a Lie epimorphism with kernel 1 (f(R)); (iii) if f(R) is a prime Lie ring and A, B are Lie ideals of R, then [f(A), f(B)] = (0) implies that either f(A) = (0) or f(B) = (0).eninfo:eu-repo/semantics/closedAccesssemiprime ringsemiprime Lie ringprime Lie ringgeneralized derivationArticle32482783310.4134/CKMS.c170019N/AWOS:0004140431000042-s2.0-85032276032Q3