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Minimal vector lattice covers

Published online by Cambridge University Press:  17 April 2009

Paul F. Conrad
Paul F. Conrad
Affiliation:
University of Kansas, Lawrence, Kansas, USA.
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Abstract

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We show that each abelian l–group G is a large l–subgroup of a minimal vector lattice V and if G is archimedean then V is unique, in fact, V is the l–subspace of (Gd)^ that is generated by G, where Gd is the divisible hull of G and (Gd)^ is the Dedekind-MacNeille completion of Gd. If G is non-archimedean then V need not be unique, even if G is totally ordered.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 35 - 39
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bernau, S.J., “Orthocompletion of lattice groups”, Proc. London Math. Soc. (3) 16 (1966), 107–130.CrossRefGoogle Scholar
[2]Conrad, Paul and McAlister, Donald, “The completion of a lattice ordered group”, J. Austral. Math. Soc. 9 (1969), 182–208.CrossRefGoogle Scholar
[3]Conrad, Paul, “Free abelian l–groups and vector lattices”, Math. Ann. (to appear).Google Scholar
[4]Fuchs, L., Partially ordered algebraic systems (Pergamon Press, Oxford, London, New York, Paris, 1963).Google Scholar