Example of an interpolation domain
type: Item
instance of: scholarly article
title: Example of an interpolation domain
zbMATH Open document ID: 1043.13003
DOI: 10.1016/S0022-4049(02)00052-X
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: A domain \(D\) is an interpolation domain if, for every choice of finitely many distinct elements \(a_1,\ldots,a_n\) of \(D\), and arbitrary \(b_1,\ldots,b_n\) in \(D\) there exists a polynomial \(f\in \text{Int}(D)\) with \(f(a_i)=b_i\) for \(1\leq i\leq n\). Here \(\text{Int}(D)\) denotes the ring of integer-valued polynomials on \(D\), i.e.~the ring of polynomials with coefficients in the quotient field of \(D\) with the property \(f(d)\in D\) for every \(d\in D\). The author gives an example of an interpolation domain whose integral closure is not an interpolation domain, thereby answering a question posed by \textit{P.-J. Cahen, J.-L. Chabert} and \textit{S. Frisch} [J. Algebra 225, No. 2, 794--803 (2000; Zbl 0990.13014)].
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 1839053
zbMATH Keywords: integer-valued polynomials
zbMATH Keywords: interpolation domain
zbMATH Keywords: integral closure
author: David C. Lantz
MaRDI profile type: Publication
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cites work: A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
description: scientific article; zbMATH DE number 1839053