On groups and fields definable in o-minimal structures
type: Item
instance of: scholarly article
title: On groups and fields definable in o-minimal structures
zbMATH Open document ID: 0662.03025
DOI: 10.1016/0022-4049(88)90125-9
author: Anand Pillay
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: It is shown that a group G definable in an o-minimal structure M (i.e. G is a definable subset of \(M^ n\) and the group operation is definable) can be definably equipped with the structure of a ``group manifold over M''. As a consequence it is shown that any field definable in an o- minimal structure is real closed or algebraically closed.
reviewed by: Anand Pillay
Mathematics Subject Classification ID: 03C60
zbMATH DE Number: 4081526
zbMATH Keywords: real closed field
zbMATH Keywords: algebraically closed field
zbMATH Keywords: o-minimal structure
zbMATH Keywords: group manifold
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90125-9
OpenAlex ID: W1980560577
cites work: Groups of small Morley rank
cites work: Definable Sets in Ordered Structures. II
cites work: On $ω_1$-categorical theories of fields
cites work: Some remarks on definable equivalence relations in O-minimal structures
cites work: First order topological structures and theories
cites work: Definable Sets in Ordered Structures. I
cites work: On Algebraic Groups of Transformations
description: scientific article; zbMATH DE number 4081526