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Vector lattices over subfields of the reals

Part of: Ordered structures

Published online by Cambridge University Press:  09 April 2009

P. Bixler ,
P. Conrad ,
W. B. Powell  and
C. Tsinakis
P. Bixler
Affiliation:
Department of Computer Science Virginia Polytechnic InstituteBlacksburg, Virginia 24061, U.S.A.
P. Conrad
Affiliation:
University of KansasLawrence, Kansas 66044, U.S.A.
W. B. Powell
Affiliation:
Oklahoma State UniversityStillwater, Oklahoma 74078, U.S.A.
C. Tsinakis
Affiliation:
Vanderbilt UniversityNashville, Tennessee 37235, U.S.A.
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Abstract

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In this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity of l-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a non-linear l-automorphism and more than one scalar multiplication. It is also shown that each l-group contains a largest archimedean convex l-subgroup which admits a unique scalar multiplication.

MSC classification

Secondary: 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 359 - 375
Copyright
Copyright © Australian Mathematical Society 1990

References

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