2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71833In this paper we generalize the well-known construction of shuffle product algebras by using mixable shuffles, and prove that any free Baxter algebra is isomorphic to a mixable shuffle product algebra. This gives an explicit construction of the free Baxter algebra, extending the work of Rota and Cartier.30 pagesRings and AlgebrasCommutative AlgebraCombinatoricsCategory Theory16A06, 47B99text