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Cauchy completion of Abelian tight Riesz groups

Published online by Cambridge University Press:  09 April 2009

B. F. Sherman
B. F. Sherman
Affiliation:
Department of Mathematics, Monash University, Clayton, 3168, Australia
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This paper concerns the completions of partially ordered groups introduced by Fuchs (1965a) and the author (to appear); the p.o. groups under consideration are, generally, abelian tight Riesz groups, and so, throughout, the word “group” will refer to an abelian group.

In section 3 we meet the cornerstone of the work, the central product theorem, by means of which we can interpret the Cauchy completion of a tight Riesz group in terms of the completion of any of its o-ideals; one particularly important case arises when the group has a minimal o-ideal. Such a minimal o-ideal is o-simple, and in section 6 the completion of an isolated o-simple tight Riesz group is shown to be a tight Riesz real vector space.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 1 , February 1975 , pp. 62 - 73
Copyright
Copyright © Australian Mathematical Society 1975

References

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