  In 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.
