Ideals and primitive elements of some relatively free Lie algebras

Let F be a free Lie algebra of finite rank over a field K . We prove that if an ideal v ~ of the algebra F / γ m + 1 F ′ contains a primitive element u ~ then the element v ~ is primitive. We also show that, in the Lie algebra F / γ 3 F ′ there exists an element v ¯ such that the ideal v ¯ contains a primitive element u ¯ but, u ¯ and v ¯ are not conjugate by means of an inner automorphism.