Which abelian groups can support a directed, interpolation order?
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- by A. M. W. Glass PDF
- Proc. Amer. Math. Soc. 31 (1972), 395-400 Request permission
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
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 395-400
- MSC: Primary 06.78; Secondary 20.00
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289389-7
- MathSciNet review: 0289389