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Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,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+C and a linear map ζ:R→C such that f(x)=g(x)+ζ(x) for all x∈R and ζ([R,R])=0 provided that A does not satisfy...