Ordered fields satisfying Pólya’s theorem

Guangxing, Zeng

doi:10.1090/S0002-9939-05-07856-1

Ordered fields satisfying Pólya’s theorem
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by Zeng Guangxing

Proc. Amer. Math. Soc. 133 (2005), 2921-2926

DOI: https://doi.org/10.1090/S0002-9939-05-07856-1

Published electronically: April 25, 2005

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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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