Continuous functions on discrete valuation rings
type: Item
instance of: scholarly article
title: Continuous functions on discrete valuation rings
zbMATH Open document ID: 0938.12003
author: Koichi Tateyama
published in: Journal of Number Theory
publication date: 1999-07-22T00:00:00Z
review text: Let \(R\) be a complete discrete valuation ring with field of fractions \(K\) and maximal ideal \({\mathfrak p}\). The author gives an explicit and simple construction of an \(R\)-base \(\{\varphi_n\), \(n=0,1,2\dots\}\) of the \(R\)-module generated by the set of all polynomial functions from \(R\) to \(R\). Using this base, he shows that when \(R/{\mathfrak p}\) is a finite field, then a function \(f\) from \(R\) into any finite extension \(F\) of \(K\) is continuous if and only if there exist (uniquely determined) elements \(a_n\in F\) such that \(\lim_{n\to\infty} a_n=0\) and \(f(a)= \sum_{n=0}^\infty a_n \varphi_n(a)\) for all \(a\) in \(R\). The above result is a generalization of Mahler's expansion theorem.
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12J20
zbMATH DE Number: 1274809
zbMATH Keywords: complete discrete valuation ring
zbMATH Keywords: \(R\)-base
zbMATH Keywords: polynomial functions
reviewed by: Sudesh Kaur Khanduja
MaRDI profile type: Publication
full work available at URL: jnth.1998.2333
OpenAlex ID: W2027737491
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DOI: 10.1006/JNTH.1998.2333
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description: scientific article; zbMATH DE number 1274809