| 关于实Hilbert环 |
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| 引用本文： | 曾广兴,戴执中. 关于实Hilbert环[J]. 数学学报, 1997, 40(2): 175-184. DOI: cnki:ISSN:0583-1431.0.1997-02-002 |
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| 作者姓名： | 曾广兴 戴执中 |
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| 作者单位： | 南昌大学数学与系统科学系 南昌330047(曾广兴)，南昌大学数学与系统科学系 南昌330047(戴执中) |
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| 基金项目： | 国家与江西省自然科学基金 |
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| 摘 要： | 通过引进“强实Hilbert环”这一概念,本文证明了,一个环A是强实Hilbert环,当且仅当多项式环A[X]是实Hilbert环,当且仅当A[X]的每个实极大理想在A上的局限是实极大的,从而文献[1]中两个主要结果被否定.此外,本文还研究了所谓的“严格的实Hilbert环”,这类环对于半代数零点定理等方面的探讨更具应用意义.
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| 关 键 词： | 实极大理想 〈V〉-根理想 实Hilbert环 强实Hilbert环 严格的实Hilbert环 |
| 收稿时间： | 1995-09-30 |
On Real Hilbert Rings |
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| Zeng Guangxing Dai Zhizhong. On Real Hilbert Rings[J]. Acta Mathematica Sinica, 1997, 40(2): 175-184. DOI: cnki:ISSN:0583-1431.0.1997-02-002 |
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| Authors: | Zeng Guangxing Dai Zhizhong |
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| Affiliation: | Zeng Guangxing Dai Zhizhong (Department of Mathematics and System Science, Nanchang University, Nanchang 330047, China) |
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| Abstract: | In this paper, by introducing the notion of a strongly real Hilbert ring, we show that (1) A ring A is a strqngly real Hilbert ring if and only if A[X] is a real Hilbert ring; and (2) A ring A is a strongly real Hilbert ring if and only if every real maximal ideal of A[X]contracts in A to a real maximal ideal. Thereby, the two main results listed in reference [1] are negated. Moreover, the so-called strictly real Hilbert rings are investigated; these rings are of significance for the discussion of the semialgebraic Nullstellensatz. |
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| Keywords: | Real maximal ideal |
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