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Divisibility of ordered groups

Published online by Cambridge University Press:  20 January 2009

I. W. Wright
I. W. Wright
Affiliation:
Monash University, Clayton, Victoria 3168, Australia Now at: Papua and New Guinea Institute of Technology, Box 793, Lae, New Guinea
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In this paper it is shown that divisibility of a complete lattice ordered (abelian) group is closely related to the existence of a sufficient number of small elements in the positive cone.

We shall denote the set of all real numbers by R which symbol will be reserved for this purpose. All terms used are as defined in Birkhoff(1). For the reader's convenience we now define the two terms most used in the sequel.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 81 - 83
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Birkhoff, G., Lattice Theory (3rd edition) (Amer. Math. Soc, 1967).Google Scholar
(2) Fuchs, L., Partially Ordered Algebraic Systems (Pergamon, 1963).Google Scholar
(3) Bernau, S. J., Unique representations of Archimedean lattice groups and normal Archimedean lattice rings, Proc. London Math. Soc. 15 (1965), 599–631.CrossRefGoogle Scholar