2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121121The operad Lie can be constructed as the operad of primitives Prim As from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincare'-Birkhoff-Witt and Cartier-Milnor-Moore. We replace As by families of free operads P, which include the operad Mag freely generated by a noncommutative non-associative binary operation and the operad of Stasheff polytopes. We obtain Poincare'-Birkhoff-Witt type theorems and collect information about the operads Prim P, e.g. in terms of characteristic functions.25pages, uses elsart.cls, paper extracted from habilitation thesis (math.RA/0407074), revised (more details in sections 2,3,4, and 6)Rings and AlgebrasCombinatorics18D50; 16W30, 17A50, 18D35text