Class number one problem for imaginary function fields: the cyclic prime power case
type: Item
instance of: scholarly article
title: Class number one problem for imaginary function fields: the cyclic prime power case
zbMATH Open document ID: 0962.11038
author: Stéphan Sémirat
published in: Journal of Number Theory
publication date: 2001-02-06T00:00:00Z
review text: Let \(\mathbb F_q\) be a finite field having \(q\) elements. In this paper, the author finds all (up to \(\mathbb F_q\)-isomorphisms) imaginary cyclic extensions of prime power degree \(K/\mathbb F_q(T)\) such that the integral closure of \(\mathbb F_q[T]\) in \(K\) is a principal ideal domain. This extends the results of \textit{R. E. MacRae} [J. Algebra 17, 243--261 (1971; Zbl 0212.53302)]. In order to do this, the author uses the results of \textit{G. Lachaud} and \textit{M. Martin-Deschamps} [Acta Arith. 56. 329--340 (1990; Zbl 0727.14019)].
reviewed by: Bruno Anglès
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 1533163
zbMATH Keywords: imaginary cyclic extensions of prime power degree
zbMATH Keywords: integral closure
zbMATH Keywords: principal ideal domain
MaRDI profile type: Publication
OpenAlex ID: W2022008709
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DOI: 10.1006/JNTH.2000.2535
description: scientific article; zbMATH DE number 1533163