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 | References | Similar Articles | Additional Information

Abstract: Rings in which each partial order can be extended to a total order are called - rings by Fuchs. We characterize - rings as subrings of algebras over the rationals that arise by freely adjoining an identity or one-sided identity to a rational vector space or by taking the direct sum of with an - field. Each real quadratic extension of the rationals is an - field.

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Additional Information

**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