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arXiv · 2002.02129

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

Prosenjit Das
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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 $ch(k) \nmid n$.

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Prosenjit Das. 2020-02-06. On cancellation of variables of the form $bT^n-a$ over affine normal domains. https://doi.org/10.1016/j.jpaa.2015.05.011

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