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Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Which abelian groups can support a directed, interpolation order?


Author: A. M. W. Glass
Journal: Proc. Amer. Math. Soc. 31 (1972), 395-400
MSC: Primary 06.78; Secondary 20.00
MathSciNet review: 0289389
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Abstract: We prove that an abelian group can support a directed, interpolation order if and only if it is torsion-free or its quotient by its torsion subgroup is noncyclic. The proof is of an elementary nature. As a consequence of the proof, it is also shown that an abelian group can support a directed, interpolation order if and only if it can support a directed, interpolation, weakly semi-isolated order. The paper is completely self-contained so as to be readable by nonspecialists.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0289389-7
PII: S 0002-9939(1972)0289389-7
Keywords: Totally ordered group, directed group, interpolation property, weakly semi-isolated group, torsion subgroup of an abelian group, rank of an abelian group, cyclic element of an abelian torsion-free group
Article copyright: © Copyright 1972 American Mathematical Society



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