Remark on ''On normal integral bases''
type: Item
instance of: scholarly article
title: Remark on ''On normal integral bases''
zbMATH Open document ID: 0577.12003
author: Fuminori Kawamoto
published in: Tokyo Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: We can easily extend Theorem 2 of [ibid. 7, 221-231 (1984; Zbl 0553.12001)] to the following theorem: Suppose that \(\ell\) is an odd prime and a \((\neq \pm 1)\) is a rational integer without \(\ell\)-th power factor such that \(a^{\ell -1}\equiv 1 mod \ell^ 2\). Then \({\mathbb{Q}}(\zeta_{\ell},^{\ell}\sqrt{a})/{\mathbb{Q}}(\zeta_{\ell})\) has always a normal integral basis.
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11S15
zbMATH DE Number: 3922786
zbMATH Keywords: tamely ramified
zbMATH Keywords: explicit generator
zbMATH Keywords: Kummer
zbMATH Keywords: extensions
zbMATH Keywords: normal integral basis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270151583
OpenAlex ID: W2018701639
DOI: 10.3836/TJM/1270151583
description: scientific article; zbMATH DE number 3922786