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Ordered fields satisfying Pólya's theorem
Author(s):
Zeng
Guangxing
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2921-2926.
MSC (2000):
Primary 12J15;
Secondary 12D15
Posted:
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  satisfies Pólya's theorem if and only if  is an archimedean ordering and  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:
10.1090/S0002-9939-05-07856-1
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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