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DIAGRAMS OF AN ABELIAN GROUP

Part of: Abelian groups

Published online by Cambridge University Press:  06 July 2009

THEODORE G. FATICONI
THEODORE G. FATICONI*
Affiliation:
Department of Mathematics, Fordham University, Bronx, NY 10458, USA (email: [email protected])
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Abstract

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In this paper, we characterize quadratic number fields possessing unique factorization in terms of the power cancellation property of torsion-free rank-two abelian groups, in terms of Σ-unique decomposition, in terms of a pair of point set topological properties of Eilenberg–Mac Lane spaces, and in terms of the sequence of rational primes. We give a complete set of topological invariants of abelian groups, we characterize those abelian groups that have the power cancellation property in the category of abelian groups, and we characterize those abelian groups that have Σ-unique decomposition. Our methods can be used to characterize any direct sum decomposition property of an abelian group.

Keywords

abelian groupspoint set topological spaceshomologyhomotopyrings and modulescategoriesfunctors

MSC classification

Secondary: 20K99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 38 - 64
Copyright
Copyright © Australian Mathematical Society 2009

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