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September 2016 Images of polynomial maps on ample fields
Michiel Kosters
Funct. Approx. Comment. Math. 55(1): 23-30 (September 2016). DOI: 10.7169/facm/2016.55.1.2

Abstract

In this article we study the following problem. Let $k$ be an infinite field and let $f \in k[x]$. Consider the evaluation map $f_k: k \to k$. Assume that $f_k$ is not surjective. Is $k \smallsetminus f_k(k)$ infinite? We give a positive answer to this question when $k$ is a perfect ample field. In fact, we prove that $|k \smallsetminus f_k(k)|=|k|$. This conclusion follows from a similar statement about finite morphisms between normal projective curves over perfect ample fields.

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Michiel Kosters. "Images of polynomial maps on ample fields." Funct. Approx. Comment. Math. 55 (1) 23 - 30, September 2016. https://doi.org/10.7169/facm/2016.55.1.2

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06862550
MathSciNet: MR3549010
Digital Object Identifier: 10.7169/facm/2016.55.1.2

Subjects:
Primary: 12J10
Secondary: 11R58

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.55 • No. 1 • September 2016
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