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The SP-hull of a Lattice-Ordered Group

Published online by Cambridge University Press:  20 November 2018

Roger D. Bleier*
Affiliation:
University of Texas, Austin, Texas
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There have been several recent papers on the subject of the P-hull and the SP-hull of an l-group (lattice-ordered group). The most natural formulation of the concepts was given by P. Conrad in [6]. T. Speed studied P-groups extensively in [11]; his work was motivated by earlier work by H. Nakano and I. Amemiya in a vector lattice setting. A. Vecksler [12] produced the SP-hull for f-rings. The ortho-completion of S. Bernau [2] is a related concept.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Baker, K., Free vector lattices, Can. J. Math. 20 (1968), 5866.Google Scholar
2. Bernau, S., Orthocompletions oj'lattice groups, Proc. London Math. Soc. 16 (1966), 107130.Google Scholar
3. Bleier, R., Archimedean vector lattices generated by two elements, Proc. Amer. Math. Soc. 39 (1973), 19.Google Scholar
4. Chambless, D., Representation of the protectable and strongly protectable hulls of a latticeordered group, Proc. Amer. Math. Soc. 34 (1972), 346350.Google Scholar
5. Chambless, D., The representation and structure of lattice-ordered groups and f-rings, Ph.D. Thesis, Tulane University, 1971.Google Scholar
6. Conrad, P., Hulls of representable l-groups and f-rings, J. Austral. Math. Soc. 16 (1973), 385415.Google Scholar
7. Conrad, P., The lateral completion of a lattice-ordered group, Proc. London Math. Soc. 19 (1969), 444486.Google Scholar
8. Conrad, P., Lattice-ordered groups, Tulane University, 1970.Google Scholar
9. Conrad, P. and D. McAlister, The completion of a lattice-ordered group, J. Austral. Math. Soc. 9 (1969), 182208.Google Scholar
10. Keimel, K., Representation de groupes et d'anneaux reticules par des sections dans des faisceaux, Ph.D. Thesis, University of Paris, 1970.Google Scholar
11. Speed, T., On lattice-ordered groups (preprint).Google Scholar
12. Vecksler, A., Structural orderability of algebras and rings, Soviet Math. Dokl. 6 (1965), 12011204.Google Scholar