On cancellation of variables of the form $bT^n-a$ over affine normal domains

Abstract

In this article we extend a cancellation theorem of D. Wright to the case of affine normal domains. We shall show that if $A$ is an algebra over a Noetherian normal domain $R$ containing a field $k$ and if $A[T ] = R^{[3]}$, then $A = R^{[2]}$ if and only if $A[T]$ has a variable of the form $bT^n - a$ for some $a, b \in A$ with $n \ge 2$ and $ch(k) \nmid n$.