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Remark on ordered abelian groups

Published online by Cambridge University Press:  17 April 2009

Donald P. Minassian
Donald P. Minassian
Affiliation:
Butler University, Indianapolis, Indiana, USA.
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Abstract

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Let N be a subgroup of the torsion-free abelian group G. Then a partial order for N is contained in one, two or uncountably many full orders for G, and a full order for nonzero N is contained in one or uncountably many full orders for G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 411 - 413
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Fuchs, L., Partially ordered algebraic systems (Pergamon, Oxford, London, New York, Paris, 1963).Google Scholar
[2]Fuchs, L. and Sasiada, E., “Note on orderable groups”, Ann. Univ. Soi. Budapest. Eötvös, Sect. Math. 7 (1964), 13–17.Google Scholar
[3]Neumann, B.H. and Shepperd, J.A.H., “Finite extensions of fully ordered groups”, Proc. Roy. Soc. London Ser. A 239 (1957), 320–327.Google Scholar