In this paper, we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew Poincaré–Birkhoff–Witt (PBW) extensions. Moreover, we find a counterexample to the conjecture proposed in [V. A. Artamonov, Quantum Polynomial, Advances in Algebra and Combinatorics (World Scientific, 2008)].
