The absolute Galois group of a pseudo real closed field with finitely many orders
type: Item
instance of: scholarly article
title: The absolute Galois group of a pseudo real closed field with finitely many orders
zbMATH Open document ID: 0595.12012
DOI: 10.1016/0022-4049(85)90052-0
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: The author gives a characterization of the absolute Galois group G(K) of a prc-field K which admits exactly e orderings (prc e-field). A field K is called prc if each K-variety which has a simple point in every real closure of K, admits a K-rational point. The author assigns to every field K with e orderings a so-called absolute Galois e-structure \({\mathcal G}(K)\) and proves that in the category of profinite e-structures the ones which are realized by prc e-fields are exactly the projective ones. A profinite e-structure is a system \({\mathcal G}=(G\); \(X_ 1,...,X_ e)\) where G is a profinite group and the \(X_ i's\) are non-empty G-orbits such that the group \(\{\) \(\tau\in G|\) \(x^{\tau}=x\}\) is cyclic of order 2. After introducing morphisms suitably, the notion of projectivity is defined as usual.
reviewed by: Alexander Prestel
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 3957248
zbMATH Keywords: pseudo real closed field
zbMATH Keywords: absolute Galois group
zbMATH Keywords: prc-field
zbMATH Keywords: orderings
zbMATH Keywords: variety
zbMATH Keywords: rational point
zbMATH Keywords: absolute Galois e-structure
zbMATH Keywords: profinite group
zbMATH Keywords: projectivity
author: Şerban A. Basarab
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90052-0
OpenAlex ID: W1968958345
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description: scientific article; zbMATH DE number 3957248