Let $R$ be an integral domain and $\alpha$ a super-primitive element of degree
$d \geq 2$ over $R$. In the preceding paper [1] we have discussed the invertibility
of an element $\alpha - a$ and the flatness of $R[\alpha]/R$. In this paper we will
give some conditions for an element $\alpha^{2} - a$ to be a unit of $R[\alpha]$ and
give a sufficient condition for the extension $R[\alpha]/R$ to be a flat extension.
Furthermore, we will prove an analogous result to Theorem 7 in [1]. Finally we will
give some results on the invertibility of a linear form $a \alpha - b$ of a Laurent
extension $R[\alpha,~\alpha^{-1}]$.