We show that every polynomial overring of the ring 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 \widehat{\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}.
Polynomial overrings of $\rm Int(\mathbbZ)$
PERUGINELLI, GIULIO
2016
Abstract
We show that every polynomial overring of the ring 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 \widehat{\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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