| 关于严实Hilbert环 |
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| 引用本文： | 曾广兴.关于严实Hilbert环[J].数学学报,1998,41(1):103-106. |
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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 |
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| 摘 要： | 在本文中，严实Ｈｉｌｂｅｒｔ环得到了更进一步的刻划．本文的主要结果是：一个环Ａ是严实Ｈｉｌｂｅｒｔ环，当且仅当多项式环Ａ［Ｘ］的每个实极大理想在Ａ上的局限是Ａ的一个极大理想，当且仅当Ａ是实Ｈｉｌｂｅｒｔ环，且Ａ［Ｘ］的每个实极大理想是极大的．
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| 关 键 词： | 严实Hilbert环，实Hilbert环，强实Hilbert环，实极大理想，＜V＞-根理想 |
| 收稿时间： | 1995-05-30 |
On Strictly Real Hilbert Rings |
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| Institution: | Zeng Guangxing (Department of Mathematics & System Science, Nanchang University, Nanchang 330047, China) |
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| Abstract: | In this paper, strictly real Hilbert rings are further investigated. In order to characterize strictly real Hilbert rings, we prove the following results: Let A be a commutative ring with 1, and let A be the polynomial ring over A in one variable X . Then (1) A is a strictly real Hilbert ring if and only if every real maximal ideal of A contracts in A to a maximal ideal;(2) A is a strictly real Hilbert ring if and only if A is a real Hilbert ring, and every real maximal ideal of A is maximal. |
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| Keywords: | Strictly real Hilbert ring Real Hilbert ring Strongly real Hilbert ring Real maximal ideal 〈 V 〉 radical ideal |
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