2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76601We describe the structure of the Grothendieck ring of projective modules of basic Hopf algebras using a positive integer determined by the composition series of the principal indecomposable projective module.Quantum AlgebraK-Theory and Homology16E20; 16W30The projective class ring of half-quantum groups at roots of unitytext