On the minimum index of a cyclic quartic field
type: Item
instance of: scholarly article
title: On the minimum index of a cyclic quartic field
zbMATH Open document ID: 0627.12003
DOI: 10.1007/BF01195105
author: Toru Nakahara
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Pour tout corps de nombres \(K/ \mathbb{Q}\), on désigne par \(\tilde m(K)\) le minimum des indices des entiers de \(K\) et par \(m(K)\) le p.g.c.d. des indices des entiers de \(K\). L'A. montre que pour tout entier \(N>0\), il existe une extension cyclique de degré 4 de \(\mathbb{Q}\) telle que \(\tilde m(K)>N\) et \(m(K)=1\), en construisant explicitement de telles familles de corps.
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 4019174
zbMATH Keywords: minimum index
zbMATH Keywords: cyclic quartic field
MaRDI profile type: Publication
cites work: Q4156851
cites work: Q3676228
cites work: On discriminants and indices of integers of an algebraic number field.
cites work: Indices in cubic fields
cites work: Q4186440
cites work: On cyclic biquadratic fields related to a problem of Hasse
cites work: On the indices and integral bases of non-cyclic but Abelian biquadratic fields
full work available at URL: https://doi.org/10.1007/bf01195105
OpenAlex ID: W2081508412
description: scientific article; zbMATH DE number 4019174