2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73030There is a natural algebra map (in fact, embedding) from the noncommutative symmetric functions NSym to the quadratic algebra Q_{\infty} of pseudoroots of polynomials. In this note, I show that it is not a coalgebra map. Hence, the Hopf algebra structure on NSym can't be extended to this important larger algebra.references added, some revisionsRings and Algebras16W30; 05E05text