2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165608A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are subsets of the set of positive integers, is a vector space endowed with an n-ary operation for each n in S and an m-ary co-operation for each m in T satisfying some compatibility and unitary relations. We prove an analogue of the Poincaré-Birkhoff-Witt theorem for these partial magmatic bialgebras.Revised version, after suggestions of the anonymous referee, 20 pagesRings and AlgebrasCombinatorics18D50; 17A50; 16W30text