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Primary Decomposition for Σ-Groups

Published online by Cambridge University Press:  20 November 2018

Don Brunker  and
Denis Higgs
Don Brunker
Affiliation:
Bureau of Industry EconomicsCanberra, A.C.T. 2600, Australia
Denis Higgs
Affiliation:
Pure Mathematics Department, University of WaterlooWaterloo, Ontario, CanadaN2L 3G1
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Abstract

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A Σ-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its p-components carries over to the case of Σ-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of Σ-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.

Keywords

20K99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 399 - 403
Copyright
Copyright © Canadian Mathematical Society 1988

References

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