| 关于弱Hilbert性质的一个问题 |
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| 引用本文： | 曾广兴. 关于弱Hilbert性质的一个问题[J]. 数学学报, 1998, 41(5): 925-930. DOI: cnki:ISSN:0583-1431.0.1998-05-002 |
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| 作者姓名： | 曾广兴 |
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| 作者单位： | 南昌大学数学系 |
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| 摘 要： | 本文证明了这样一个主要结果：设（Ｋ，Ｓ）和（Ｋ，Ｓ）都是亚序域，且（Ｋ，Ｓ）是（Ｋ，Ｓ）的有限生成扩张，则当Ｋ在Ｋ上是超越时，（Ｋ，Ｓ）具有弱Ｈｉｌｂｅｒｔ性质．这一结果否定地回答了作者在文献［１］中所提的一个公开问题．此外，一些关于弱Ｈｉｌｂｅｒｔ性质的结果被建立．
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| 关 键 词： | 序域，亚序域，弱Hilbert性质，正定多项式 |
A Problem About the Weak Hilbert Property |
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| Zeng Guangxing. A Problem About the Weak Hilbert Property[J]. Acta Mathematica Sinica, 1998, 41(5): 925-930. DOI: cnki:ISSN:0583-1431.0.1998-05-002 |
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| Authors: | Zeng Guangxing |
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| Affiliation: | Zeng Guangxing (Department of Mathematics, Nanchang University, Nanchang 330047, China) |
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| Abstract: | In this paper, the main result is proved: Let both(K,S) and (K *, S *) be preordered fields, and let (K *, S *) be a finitely generated extension of (K,S). If K * is transcendental over K, then (K *, S *) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference . Moreover, some results on the weak Hilbert property are established. |
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| Keywords: | Order field Preordered field The weak Hilbert property Positive definite polynomial |
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