Minimal vector lattice covers

Roger D. Bleier

doi:10.1017/S0004972700047286

Abstract

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We show that each archimedean lattice-ordered group is contained in a unique (up to isomorphism) minimal archimedean vector lattice. This improves a result of Paul F. Conrad appearing previously in this Bulletin. Moreover, we show that this relationship between archimedean lattice-ordered groups and archimedean vector lattices is functorial.

References

[1]Birkhoff, Garrett, Lattice theory (Colloquium Publ. 25, Amer. Math. Soc., Providence, 3rd ed., 1967).Google Scholar

[2]Conrad, Paul F., “Free abelian l-groups and vector lattices”, Math. Ann. 190 (1971), 306–312.CrossRef Google Scholar

[3]Conrad, Paul F., “Minimal vector lattice covers”, Bull. Austral. Math. Soc. 4 (1971), 35–39.CrossRef Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Minimal vector lattice covers

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