A problem about the weak Hilbert property |
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Authors: | Zeng Guangxing |
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Institution: | (1) Department of Mathematics and Systems Science, Nanchang University, 330047 Nanchang, China |
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Abstract: | In this paper, we prove the main result: Let both (K, S) and (K
*,S
*) be preordered fields, and let (K
*,S
*) be a finitely generated extension of (K, S). IfK
* is transcendental overK, then (K
*,S
*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference 1]. Moreover,
some results on the weak Hilbert property are established.
Project supported by National Natural Science Foundation of China |
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Keywords: | Ordered field Preordered field The weak Hilbert property Positive definite polynomial |
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