2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59072In previous joint work with Frohman and Lofaro a noncommutative generalization of the A-polynomial of a knot was introduced, consisting of a finitely generated ideal of polynomials (the noncommutative A-ideal) in the quantum plane. The present paper shows that the noncommutative A-ideal of a knot, together with finitely many of its colored Jones polynomials determines all other colored Jones polynomials. Also, for particular knots, such as the unknot and the trefoil, the noncommutative A-ideal completely determines all colored Jones polynomials.LATEX, 6 pagesQuantum AlgebraGeometric Topology57M27text