Automorphism polynomials in cyclic cubic extensions
type: Item
instance of: scholarly article
title: Automorphism polynomials in cyclic cubic extensions
zbMATH Open document ID: 0876.11048
author: Robin Chapman
published in: Journal of Number Theory
publication date: 1997-10-28T00:00:00Z
review text: The author first describes cyclic sextic extensions \(K/k\) with \(k\) being a field of characteristic \(\neq3\) under the assumption that \(\zeta_3\), the cubic root of unity, is contained in \(K\) but not in \(k\), and then determines the minimal polynomial of a generator of \(K/k\) and the generating automorphism of the Galois group. This permits the elimination of the use of computers in the proofs of the main results of \textit{P. Morton} [J. Number Theory 49, 183-208 (1994; Zbl 0810.12003)]. The case when \(k\) is either of characteristic 3 or contains \(\zeta_3\) is treated briefly at the end of the paper.
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 11C08
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 980270
zbMATH Keywords: cubic extensions
zbMATH Keywords: sextic extensions
zbMATH Keywords: automorphism polynomials
zbMATH Keywords: Galois group
Wikidata QID: Q57918173
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: jnth.1996.0149
OpenAlex ID: W2008936491
DOI: 10.1006/JNTH.1996.0149
description: scientific article; zbMATH DE number 980270