Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T11:05:31.836Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bourbaki, N., Elements of Mathematics HI, General Topology Hermann, Paris, and Addison-Wesley, Reading, Mass., 1966.Google Scholar
2. Brunker, D. M. S., Topics in the Algebra of Axiomatic Infinite Sums Ph.D. thesis, University of Waterloo, 1980.Google Scholar
3. Higgs, D., Axiomatic infinite sums — an algebraic approach to integration theory Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces, Contemporary Mathematics Vol. 2, pp. 205–212, American Mathematical Society, Providence, R.I., 1980.Google Scholar
4. Morris, S. A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups Cambridge University Press, Cambridge, 1977.Google Scholar
5. Wylie, S., Intercept-finite cell complexes in Algebraic Geometry and Topology a Symposium in honor of S. Lefschetz, Princeton Mathematics Series No. 12, pp. 389–399, Princeton University Press, Princeton, N.J., 1957.Google Scholar