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Compatible Tight Riesz Orders

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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N. R. Reilly has obtained an algebraic characterization of the compatible tight Riesz orders that can be supported by certain partially ordered groups [13; 14]. The purpose of this paper is to give a “geometric“ characterization by the use of ordered permutation groups. Our restrictions on the partially ordered groups will likewise be geometric rather than algebraic. Davis and Bolz [3] have done some work on groups of all order-preserving permutations of a totally ordered field; from our more general theorems, we will be able to recapture their results.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 186 - 200
Copyright
Copyright © Canadian Mathematical Society 1976

References

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