| 关于素中心的正则环 |
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| 引用本文： | 杜先能,葛茂荣.关于素中心的正则环[J].安徽大学学报(自然科学版),2000,24(3):23-26. |
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| 作者姓名： | 杜先能 葛茂荣 |
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| 作者单位： | 安徽大学数学系，安徽合肥 230039 |
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| 基金项目： | the National Natural Science Foundation of China unde;rGrant19771070; |
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| 摘 要： | 如果Ｒ是具有素中心的环，则Ｒ是ＳＦ－环，当且仅当Ｒ是正则环，也肖且仅当Ｒ是强正则环。这成立的充要条件是对每个平坦左Ｒ－模Ｍ及φ∈ＥｎｄＲＭ，Ｓｏｃ（Ｍ／Ｉｍφ）是平坦。我们同时证明了若正则环Ｒ具有素中心，则所有单左（右）Ｒ－模是内射的。
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| 关 键 词： | 正则环 强正则环 SF-环 素中心 |
| 文章编号： | 1000-2162(2000)03-0023-04 |
On Regular Rings with Prime Centers |
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| DU Xian-neng,GE Mao-rong.On Regular Rings with Prime Centers[J].Journal of Anhui University(Natural Sciences),2000,24(3):23-26. |
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| Authors: | DU Xian-neng GE Mao-rong |
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| Abstract: | In this paper we show that if R is a ring having a prime center then R is SF- ring if and only if R is a regular ring and also if and only if R is a strongly regular rings, which is supported if and only if (M/Imψ) is flat for each flat left R - medule M and each ψ∈ EndRM .We also show that if R is a regular ring having a prime center then all simple left (right) R - modules are injective. |
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| Keywords: | regular ring strongly regular ring SF-ring prime center |
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