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.
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.
基金
the National -Natural Science Foundation of China （No. 10571026）
the Natural Science Foundation of Jiangsu Province （No. 2005207）.
