title: Ideals and primitive elements of some relatively free Lie algebras.
abstract: Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism.
authors.affiliation: Department of Mathematics, Çukurova University, 01330 Adana, Turkey.
authors.forename: Naime
authors.initials: N
authors.lastname: Ekici
authors.affiliation: Department of Mathematics, Çukurova University, 01330 Adana, Turkey.
authors.forename: Zerrin
authors.initials: Z
authors.lastname: Esmerligil
authors.affiliation: Department of Mathematics, Çukurova University, 01330 Adana, Turkey.
authors.forename: Dilek
authors.initials: D
authors.lastname: Ersalan
keywords: Free Lie algebra; Free nilpotent; Ideal; Lower central series; Primitive element