Ordered fields with the dense orbits property
type: Item
instance of: scholarly article
title: Ordered fields with the dense orbits property
zbMATH Open document ID: 0533.12018
DOI: 10.1016/0022-4049(83)90059-2
published in: Journal of Pure and Applied Algebra
publication date: 1983-01-01T00:00:00Z
review text: For a formally real field K let X(K) be the space of orderings. The automorphism group Aut(K) of K operates on X(K). K is said to have the 'dense orbits property' (DOP) if for all \(\alpha\in X(K)\) the orbit of \(\alpha\) is dense in X(K). The study of such fields, which was begun in \textit{D. W. Dubois} and the second author [Contemp. Math. 8, 265-288 (1982; Zbl 0484.12003)], is continued here. The main question considered is the behavior of the DOP under purely transcendental and under algebraic field extensions. Proposition 1.5 is false.
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 12F05
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 14Pxx
zbMATH DE Number: 3845714
zbMATH Keywords: ordered fields
zbMATH Keywords: dense orbits property
zbMATH Keywords: automorphisms acting on spaces of orderings
zbMATH Keywords: behavior under field extensions
zbMATH Keywords: formally real field
author: Jose Manuel Gamboa
author: Tomas Recio
reviewed by: Niels Schwartz
MaRDI profile type: Publication
full work available at URL: 0022-4049(83)90059-2
OpenAlex ID: W2053068943
cites work: Note on Artin’s solution of Hilbert’s 17th problem
cites work: Order extensions and real algebraic geometry
cites work: Q4182814
cites work: Q3884218
cites work: Q4129550
cites work: Q3340956
cites work: Ordered fields and sign-changing polynomials.
Recommended article: A remark on fields with the dense orbits property
Recommended article: Ordered fields satisfying Pólya’s theorem
Recommended article: Ordered fields satisfying Rolle's theorem
Recommended article: Ordered differential fields
Recommended article: Lattice-ordered fields determined by \(d\)-elements
Recommended article: Theory of ordered fields
description: scientific article; zbMATH DE number 3845714