| On UR-Rings |
| Received:March 20, 2007 Revised:November 22, 2007 |
| Key Words:
clean rings $G$-clean rings regular rings $(S,2)$-rings UR-rings.
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| Fund Project:the National Natural Science Foundation of China (No.0571026); the Natural Science Foundation of Jiangsu Province (No.2005207). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.02.020 |
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