| 应志领,陈建龙.关于UR-环[J].数学研究及应用,2009,29(2):355~361 |
| 关于UR-环 |
| On UR-Rings |
| 投稿时间：2007-03-20 修订日期：2007-11-22 |
| DOI：10.3770/j.issn:1000-341X.2009.02.020 |
| 中文关键词: clean环 G-clean环 正则环 $(S,2)$-环 UR-环. |
| 英文关键词:clean rings $G$-clean rings regular rings $(S,2)$-rings UR-rings. |
| 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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| 中文摘要: |
| 一个环称为UR-环如果环中的每个元素是一个可逆元和一个正则元之和.它是正则环、 clean环和(S,2)-环的共同推广.我们研究了这些环之间的关系,推广了clean环和(S,2)-环的一些性质并且考虑了UR-环的扩张问题. |
| 英文摘要: |
| 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 $(S,2)$-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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