Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-12T05:29:29.093Z Has data issue: false hasContentIssue false
  • English
  • Français

A final remark on extending to strict total orders in modules

Published online by Cambridge University Press:  17 April 2009

Isidore Fleischer
Isidore Fleischer
Affiliation:
Département de Mathématiques, Université de Montréal, Montréal, Canada.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The remark is that the recent work in this Bulletin dealing with the extension of a partial to a total strict order on a module over a partially ordered ring falls under standard order extension results for operator groups once it is noted that the added requirement of strictness just comes to injective operation of the positive scalars. These standard results are in turn generalized to a universal algebra setting.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 137 - 140
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Fuchs, L., Partially ordered algebraic systems (Pergamon, Oxford, London, New York, Paris, 1963).Google Scholar
[2]Fuchs, L., “On partially ordered algebras I”, Colloq. Math. 14 (1966), 115–130.CrossRefGoogle Scholar
[3]Lorenzen, Paul, “Teilbarkeitstheorie in Bereichen”, Math. Z. 55 (1952), 269–275.CrossRefGoogle Scholar
[4]Ribenboim, P., “On the extension of orders in ordered modules”, Bull. Austral. Math. Soc. 2 (1970), 81–88.CrossRefGoogle Scholar
[5]Ribenboim, P., “On the extension of orders in ordered modules: Corrigenda”, Bull. Austral. Math. Soc. 4 (1971), 288.CrossRefGoogle Scholar
[6]Spoerel, D., “A remark on Ribenboim's paper ‘On the extension of orders in ordered modules’”, Bull. Austral. Math. Soc. 6 (1972), 251–253.CrossRefGoogle Scholar