On generalized Lie derivations of Lie ideals of prime algebras

Let AA be a prime algebra of characteristic not 2 with extended centroid CC, let RR be a noncentral Lie ideal of AA and let BB be the subalgebra of AA generated by RR. If f,d:R→Af,d:R→A are linear maps satisfying thatf([x,y])=f(x)y-f(y)x+xd(y)-yd(x)forallx,y∈R,then there exist a generalized derivation g:B→AC+Cg:B→AC+C and a linear map ζ:R→Cζ:R→C such that f(x)=g(x)+ζ(x)f(x)=g(x)+ζ(x) for all x∈Rx∈R and ζ([R,R])=0ζ([R,R])=0 provided that AA does not satisfy the standard identity of degree 18.