Pólya and Newtonian function fields
type: Item
instance of: scholarly article
title: Pólya and Newtonian function fields
zbMATH Open document ID: 1141.11057
author: David Adam
published in: Manuscripta Mathematica
publication date: 2008-07-01T00:00:00Z
review text: Let \(K/\mathbb{F}_q(T)\) be a finite extension of the field of rational functions over a finite field \(\mathbb{F}_q\), and let \(O_K\) be the integral closure of \(\mathbb{F}_q[T]\) in \(K\). Moreover let \(Int(O_K)\) denotes the \(O_K\)-module of \(K\)-polynomials \(f\) with \(f(O_K)\subset O_K\). The field \(K\) is called a Pólya field, if \(\text{Int}(O_K)\) has a basis \(f_0,f_1,\dots\) with \(\deg f_n=n\) for every \(n\). The author characterizes Kummerian and Artin-Schreier-Witt extensions with this property and shows that every cyclotomic extension has it as well.
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 5294771
zbMATH Keywords: function field
zbMATH Keywords: integral polynomial
zbMATH Keywords: Pólya field
zbMATH Keywords: regular basis
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: s00229-008-0173-z
OpenAlex ID: W2058083004
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DOI: 10.1007/S00229-008-0173-Z
description: scientific article; zbMATH DE number 5294771