| 关于UR-环 |
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| 引用本文： | 应志领,陈建龙. 关于UR-环[J]. 数学研究及应用, 2009, 29(2): 355-361 |
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| 作者姓名： | 应志领 陈建龙 |
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| 作者单位： | 东南大学数学系, 江苏 南京 210096;东南大学数学系, 江苏 南京 210096 |
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| 基金项目： | 国家自然科学基金(No.10571026); 江苏省自然科学基金(No.2005207). |
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| 摘 要： | A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.
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| 关 键 词： | UR-环 清洁环 规则环 环论 |
| 收稿时间： | 2007-03-20 |
| 修稿时间： | 2007-11-22 |
On UR-Rings |
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| YING Zhi Ling and CHEN Jian Long. On UR-Rings[J]. Journal of Mathematical Research with Applications, 2009, 29(2): 355-361 |
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| Authors: | YING Zhi Ling and CHEN Jian Long |
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| Affiliation: | Department of Mathematics, Southeast University, Jiangsu 210096, China;Department of Mathematics, Southeast University, Jiangsu 210096, China |
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| Abstract: | A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and $(S,2)$-rings. Some relations of these rings are studied and several properties of clean rings and $(S,2)$-rings are extended. Ring extensions of UR-rings are also investigated. |
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| Keywords: | clean rings $G$-clean rings regular rings $(S,2)$-rings UR-rings. |
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