Let L be a finitely generated free Lie p-algebra and ‹a› an ideal generated by a ϵ L. It is proved that L/‹a› is free if and only if ‹a› is primitive (i.e. a belongs to some set of free generators of L). Earlier analogues theorems were proved for some objects, for example, for groups, Lie algebras, free algebras and so on.

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 35-40