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arXiv · 1503.06035

Polynomial overrings of ${\rm Int}(\mathbb Z)$

Jean-Luc Chabert·Giulio Peruginelli
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Abstract

We show that every polynomial overring of the ring ${\rm Int}(\mathbb Z)$ of polynomials which are integer-valued over $\mathbb Z$ may be considered as the ring of polynomials which are integer-valued over some subset of $\hat{\mathbb{Z}}$, the profinite completion of $\mathbb Z$ with respect to the fundamental system of neighbourhoods of $0$ consisting of all non-zero ideals of $\mathbb Z.$

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Jean-Luc Chabert, Giulio Peruginelli. 2015-03-20. Polynomial overrings of ${\rm Int}(\mathbb Z)$. https://doi.org/10.1216/jca-2016-8-1-1

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