| Ideal-comparability over Regular Rings |
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| 作者姓名： | Huan Yin CHEN Miao Sen CHEN |
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| 作者单位： | Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| 基金项目： | This work is supported by the National Natural Science Foundation of China （Grant No. 19801012） and the Ministry of Education of China （[2000] 65） |
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| 摘 要： | We introduce the concept of ideal-comparability condition for regular rings. Let I be an ideal of a regular ring R. If R satisfies the I-comparability condition, then R is one-sided unit-regular if and only if so is R/I. Also, we show that a regular ring R satisfies the general comparability if and only if the following hold： （1） R/I satisfies the general comparability; （2） R satisfies the general I-comparability condition; （3） The natural map B（R） → B（R/I） is surjective.
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| 关 键 词： | 理想相似性 规则环 映射 存在性 |
| 收稿时间： | 2003-02-19 |
| 修稿时间： | 2003-02-192003-08-06 |
Ideal–comparability over Regular Rings |
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| Huan Yin CHEN Miao Sen CHEN.Ideal-comparability over Regular Rings[J].Acta Mathematica Sinica,2006,22(2):417-424. |
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| Authors: | Huan Yin Chen Miao Sen Chen |
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| Institution: | (1) Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| Abstract: | We introduce the concept of ideal–comparability condition for regular rings. Let I be an
ideal of a regular ring R. If R satisfies the I–comparability condition, then R is one–sided unit–regular
if and only if so is R / I. Also, we show that a regular ring R satisfies the general comparability if
and only if the following hold: (1) R / I satisfies the general comparability; (2) R satisfies the general
I–comparability condition; (3) The natural map B(R) → B(R / I) is surjective.
This work is supported by the National Natural Science Foundation of China (Grant No. 19801012) and the
Ministry of Education of China (2000] 65) |
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| Keywords: | Ideal-Comparability Regular Rings |
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