Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T07:23:46.907Z Has data issue: false hasContentIssue false
  • English
  • Français

The vector lattice cover of certain partially ordered groups

Part of: Ordered structures Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

G. Buskes  and
A. Van Rooij
G. Buskes
Affiliation:
The University of Mississippi, College of Liberal Arts University, MS 38677, USA
A. Van Rooij
Affiliation:
Catholic UniversityToernooiveld, 6525 ED Nijmegen, The Netherlands
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.

In this paper we introduce the notion of Riesz homomorphism on Archimedean directed partially ordered groups and use it to study the vector lattice cover of such groups.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices 06F15: Ordered groups

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 3 , June 1993 , pp. 352 - 367
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Anderson, M. and Feil, R., Lattice ordered groups, an introduction (D. Reidel Publishing Company, 1987).Google Scholar
[2]Birkhoff, G., Lattice theory, 3rd edition, Colloquium Publications 25 (Amer. Math. Soc., Providence, 1984).Google Scholar
[3]Bleier, R. D., ‘Minimal vector lattice covers’, Bull. Aust. Math. Soc. 5 (1971), 331–335.CrossRefGoogle Scholar
[4]Buskes, G. and van Rooij, A., ‘Hahn-Banach for Riesz homomorphisms’, Indag. Math. A 92 (1989), 25–34.CrossRefGoogle Scholar
[5]Buskes, G. and Van Rooij, A., ‘The Archimedean 1-group tensor product’, preprint.Google Scholar
[6]Conrad, P. F., ‘Minimal vector lattice covers’, Bull. Austral. Math. Soc. 4 (1971), 35–39.CrossRefGoogle Scholar
[7]Conrad, P. F., ‘The hulls of representable 1-groups and f-rings’, J. Austral. Math. Soc. (Series A) 16 (1973), 385–415.CrossRefGoogle Scholar
[8]Fremlin, D., Topological Riesz spaces and measure theory (Cambridge University Press, London, 1974).CrossRefGoogle Scholar
[9]Jameson, G., Ordered linear spaces, Lecture Notes in Math. 141 (Springer, Berlin, 1970).CrossRefGoogle Scholar
[10]Wickstead, A. W., ‘The Spectrum of an R-homomorphism’, J. Austral. Math. Soc. (Series A) 23 (1977), 42–45.CrossRefGoogle Scholar
[11]Wickstead, A. W., ‘Relatively central operators on Archimedean vector lattices I’, Proc. Roy. Irish Acad. Sect. A 80 (1980), 191–208.Google Scholar