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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of preordered fields with the weak Hilbert property


Author: Guangxin Zeng
Journal: Proc. Amer. Math. Soc. 104 (1988), 335-342
MSC: Primary 12D15; Secondary 11E25, 11E81, 12J15
MathSciNet review: 962795
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Abstract | References | Similar Articles | Additional Information

Abstract: By introducing a new notion "local density", we show the following result: Let $ (K,S)$ be a preordered field, then $ (K,S)$ has the weak Hilbert property if and only if $ (K,S)$ is locally dense. From this, a theorem of McKenna in reference [1] and one of Prestel in reference [2] will be easily proved.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962795-2
PII: S 0002-9939(1988)0962795-2
Keywords: Preordered fields, the weak Hilbert property, definite rational functions, local density
Article copyright: © Copyright 1988 American Mathematical Society