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An Application of Ultraproducts to Lattice-Ordered Groups

Published online by Cambridge University Press:  20 November 2018

A. M. W. Glass
A. M. W. Glass*
Affiliation:
Bowling Green State University, Bowling Green, Ohio
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Using ultraproducts, N. R. Reilly proved that if G is a representable lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a total order which induces ≺ on J (see [5]). In [4], H. A. Hollister proved that a group G admits a total order if and only if it admits a representable order and, moreover, every latticeorder on a group is the intersection of right total orders. The purpose of this paper is to provide a partial converse, viz: if G is a lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a right total order which induces ≺ on J.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1063 - 1064
Copyright
Copyright © Canadian Mathematical Society 1972

References

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