2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69377We prove the existence of a basis of Poincare-Birkhoff-Witt type for braided Hopf algebras R generated by a braided subspace V of P(R) if the braiding on V fulfils a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple U_q(sl_2) modules.36 pages, uses ams latexQuantum AlgebraRings and Algebrastext