On the Annihilating polynomial of the Colored Jones Polynomial for Some Links

In this paper, we consider polynomials and ideals obtained from the colored Jones polynomial in both commutative and noncommutative cases. In the commutative case, this ideal contains polynomials that can be regarded as the link version of the $A$-polynomial; in the noncommutative case, it consists of annihilating polynomials of the colored Jones polynomial and can be regarded as the link version of the $A_q$-polynomial. Moreover, we formulate the link version of the AJ conjecture.