Formally real fields with a simple description of the absolute Galois group
type: Item
instance of: scholarly article
title: Formally real fields with a simple description of the absolute Galois group
zbMATH Open document ID: 0618.12020
DOI: 10.1007/BF01171034
author: T. M. Viswanathan
author: Antonio Engler
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155158
review text: Let R be a real closed field and k a subfield of R maximal with respect to the exclusion of some fixed element \(\alpha\in R\). The authors give a complete description of the absolute Galois group G(k) of such a field k. It turns out that there are essentially three types of profinite groups occurring, all of which are quite simple to describe. The authors also prove that, if such a group occurs as the absolute Galois group of a field k, then k admits a real closure R and is a maximal subfield of R excluding a fixed element \(\alpha\in R\).
reviewed by: Alexander Prestel
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 4002231
zbMATH Keywords: real closed field
zbMATH Keywords: absolute Galois group
zbMATH Keywords: profinite groups
MaRDI profile type: Publication
cites work: Euklidische Körper und euklidische Hüllen von Körpern.
cites work: Quadratic forms and the u-invariant
cites work: Quadratic Forms Over Formally Real Fields and Pythagorean Fields
cites work: On some Hasse principles over formally real fields
cites work: Digging holes in algebraic closures à la Artin. II
cites work: Real fields with small Galois groups
cites work: Unendliche algebraische Zahlkörper, über denen jede Gleichung auflösbar von beschränkter Stufe ist
cites work: Q5675788
cites work: Q3340956
cites work: Q5666659
cites work: Q5625306
cites work: Quadratic forms and profinite 2-groups
cites work: When are Witt rings group rings? II
OpenAlex ID: W2064450351
description: scientific article; zbMATH DE number 4002231