| 适合无限维实零点定理的序域之结构Ⅰ |
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| 引用本文： | 曾广兴. 适合无限维实零点定理的序域之结构Ⅰ[J]. 数学学报, 1999, 42(1): 125-132. DOI: cnki:ISSN:0583-1431.0.1999-01-019 |
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| 作者姓名： | 曾广兴 |
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| 作者单位： | ：南昌大学数学与系统科学系 南昌 330047 |
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| 摘 要： | 本文的目的是建立适合无限维实零点定理的序域的结构定理．作为预备工作，文章的第一部分研究一类无秩为d的裂缝的序群，这里d是无限基数．藉助于Hahn嵌入定理，本文给出了无秩为d的裂缝的序群的结构．
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| 关 键 词： | 无限维实零点定理 序域 序群 裂缝 |
| 修稿时间： | :1998-01-0 |
On Structure of Ordered Fields Satisfying the Infinite-dimensional Real Nullstellensatz I |
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| Affiliation: | Zeng Guangxing(Department of Mathematics and Systems Science,Nanchong University,Nanchang 330047,P.R. China) |
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| Abstract: | The purpose of this paper is to establish a theorem on structure of ordered fields satisfying the infinite-dimensional real Nullstellensatz. For the preliminaries, in the first part of this paper, a class of ordered groups, which have no gap of rank d for an infinite cardinal number d, is investigated. With the aid of Hahn Embeding Theorem,we give the structure of ordered groups without gap of rank d for an infinite cardinal numberd. |
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