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Ordered fields satisfying Pólya's theorem


Author: Zeng Guangxing
Journal: Proc. Amer. Math. Soc. 133 (2005), 2921-2926
MSC (2000): Primary 12J15; Secondary 12D15
DOI: https://doi.org/10.1090/S0002-9939-05-07856-1
Published electronically: April 25, 2005
MathSciNet review: 2159770
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Abstract: The purpose of this paper is to characterize ordered fields satisfying Pólya's theorem on positive representations of polynomials. As a main result, it is proved that an ordered field $(F,\le)$ satisfies Pólya's theorem if and only if $\le$ is an archimedean ordering and $F$ is a real closed field.


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Additional Information

Zeng Guangxing
Affiliation: Department of Mathematics, Nanchang University, Jiangxi Province, Nanchang 330047, People’s Republic of China
Email: zenggx@ncu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-05-07856-1
Keywords: Ordered field, P\'olya's theorem, archimedean ordering, real closed field
Received by editor(s): March 3, 2004
Received by editor(s) in revised form: June 10, 2004
Published electronically: April 25, 2005
Additional Notes: This work was partially supported by a National Key Basic Research Project of China (Grant No. 2004CB318003).
Communicated by: Lance W. Small
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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