Irrational ordered groups
type: Item
instance of: scholarly article
title: Irrational ordered groups
zbMATH Open document ID: 0654.06015
DOI: 10.1007/BF00714478
author: W. Charles Holland
author: Dwight P. Smith
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: The authors deal with the ordered set \(I\) of irrational numbers which is groupable. In Theorem 4 they characterize those ordered groups carried by \(I\) in terms of their convex subgroups. They also make a number of observations about the possible group structure of ordered groups carried by \(I\). The resulting ordered group is severely restricted in its group structure and in the structure of its set of convex subgroups.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06A15
zbMATH DE Number: 4066974
zbMATH Keywords: ordered set
zbMATH Keywords: irrational numbers
zbMATH Keywords: ordered groups
zbMATH Keywords: convex subgroups
MaRDI profile type: Publication
cites work: Groupes et anneaux reticules
cites work: Extensions of Ordered Groups and Sequence Completion
cites work: Wreath products of ordered permutation groups
cites work: Lawless order
cites work: Q5848208
cites work: Q3949052
description: scientific article; zbMATH DE number 4066974