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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of rings in which each partial order is contained in a total order


Author: Stuart A. Steinberg
Journal: Proc. Amer. Math. Soc. 125 (1997), 2555-2558
MSC (1991): Primary 06F25
MathSciNet review: 1401754
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Abstract: Rings in which each partial order can be extended to a total order are called $O^\ast $- rings by Fuchs. We characterize $O^\ast $- rings as subrings of algebras over the rationals that arise by freely adjoining an identity or one-sided identity to a rational vector space $N$ or by taking the direct sum of $N$ with an $O^\ast $- field. Each real quadratic extension of the rationals is an $O^\ast $- field.


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Stuart A. Steinberg
Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606-3390
Email: ssteinb@uoft02.utoledo.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03933-6
Received by editor(s): April 9, 1996
Communicated by: Lance W. Small
Article copyright: © Copyright 1997 American Mathematical Society