2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150867The notion of a coalgebra-Galois extension is defined as a natural generalisation of a Hopf-Galois extension. It is shown that any coalgebra-Galois extension induces a unique entwining map $ψ$ compatible with the right coaction. For the dual notion of an algebra-Galois coextension it is also proven that there always exists a unique entwining structure compatible with the right action.21 pages, LaTeX, uses amssymb. Major revision. Version to appear in Commun. AlgebraQuantum AlgebraRings and Algebras16W30 17B37 81R50text