| On Weakly $r$-Clean Rings |
| Received:October 13, 2016 Revised:May 17, 2017 |
| Key Words:
$r$-clean rings weakly clean rings weakly $r$-clean rings regular rings
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11401009; 11326062). |
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| Abstract: |
| As generalization of $r$-clean rings and weakly clean rings, we define a ring $R$ is weakly $r$-clean if for any $a\in R$ there exist an idempotent $e$ and a regular element $r$ such that $a=r+e$ or $a=r-e$. Some properties and examples of weakly $r$-clean rings are given. Furthermore, we prove the weakly clean rings and weakly $r$-clean rings are equivalent for abelian rings. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.05.005 |
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