2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115167For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms of these operators for two and three dimensional algebras are computed. A FRT bialgebra for one of these families is presented. Solutions for the one-parameter quantum Yang-Baxter equation are derived and a Yang-Baxter system constructed.13 pages, LaTeXQuantum AlgebraRings and Algebras16W30; 81R50text