关于严实Hilbert环 |
| |
引用本文: | 曾广兴. 关于严实Hilbert环[J]. 数学学报, 1998, 41(1): 103-106 |
| |
作者姓名: | 曾广兴 |
| |
作者单位: | 南昌大学数学与系统科学系 |
| |
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.
|
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 |
| |
Affiliation: | Zeng Guangxing (Department of Mathematics & System Science, Nanchang University, Nanchang 330047, China) |
| |
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. |
| |
Keywords: | Strictly real Hilbert ring Real Hilbert ring Strongly real Hilbert ring Real maximal ideal 〈 V 〉 radical ideal |
本文献已被 维普 等数据库收录! |
| 点击此处可从《数学学报》浏览原始摘要信息 |
|
点击此处可从《数学学报》下载全文 |