On cancellation of variables of the form $b{T}^n-a$ 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 $b{T}^n-a$ for some $a,b\in A$ with $n\ge 2$ and $ch(k)\nmid n$.

10 pages

References in corpus (1)

• A Note on Residual Variables of an Affine Fibration