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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
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Abstract

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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
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