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Habiro gave principal ideals of $\mathbb{Z}[q,q^{-1}]$ in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of $\mathbb{Z}[q,q^{-1}]$ generated by several elements. In this paper, we prove that these ideals also are principal, each generated by a product of cyclotomic polynomials.