A remark on quaternion extensions of the rational p-adic field
type: Item
instance of: scholarly article
title: A remark on quaternion extensions of the rational p-adic field
zbMATH Open document ID: 0732.11065
author: Genjiro Fujisaki
published in: Proceedings of the Japan Academy. Series A
publication date: 1990-01-01T00:00:00Z
review text: Let F be a rational p-adic field \({\mathbb{Q}}_ p\). There exists a Galois quaternion extension of \(F={\mathbb{Q}}_ p\) if and only if \(p\equiv 3 mod 4\) or \(p=2\). There are introduced all quaternion extensions of \({\mathbb{Q}}_ p\) in a fixed algebraic closure of \({\mathbb{Q}}_ p\).
Mathematics Subject Classification ID: 11S20
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12F05
zbMATH DE Number: 4210281
zbMATH Keywords: rational p-adic field
zbMATH Keywords: Galois quaternion extension
MaRDI profile type: Publication
full work available at URL: pjaa.66.257
OpenAlex ID: W2067121775
cites work: An elementary construction of Galois quaternion extension
cites work: Q3032353
cites work: Über Normalkörper mit Quaternionengruppe
cites work: Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf.
DOI: 10.3792/PJAA.66.257
description: scientific article; zbMATH DE number 4210281