A construction of an ordered division ring with a rank one valuation
type: Item
instance of: scholarly article
title: A construction of an ordered division ring with a rank one valuation
zbMATH Open document ID: 0677.16025
author: Ka Hin Leung
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \((k,P_ k)\) be an ordered field and \(\Gamma\) be a dense additive subgroup of \({\mathbb{R}}\). We construct a noncommutative ordered division ring (D,P) and a compatible valuation v on (D,P) such that (i) the value group of v is \(\Gamma\) and (ii) the residue division ring \((\bar D_ v,\bar P_ v)\) is order isomorphic to \((k,P_ k)\). This problem is interesting, because in effect, we are constructing the `simplest' or in some sense the smallest noncommutative ordered division ring.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 16K40
zbMATH DE Number: 4108952
zbMATH Keywords: ordered field
zbMATH Keywords: noncommutative ordered division ring
zbMATH Keywords: compatible valuation
zbMATH Keywords: value group
MaRDI profile type: Publication
full work available at URL: pjm.1991.147.139
OpenAlex ID: W1971559397
DOI: 10.2140/PJM.1991.147.139
description: scientific article; zbMATH DE number 4108952