| 弱$r$-Clean环 |
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| 引用本文： | 高汉鹏,殷晓斌.弱$r$-Clean环[J].数学研究及应用,2017,37(5):543-549. |
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| 作者姓名： | 高汉鹏 殷晓斌 |
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| 作者单位： | 安徽师范大学数学计算机科学学院, 安徽 芜湖 241000,安徽师范大学数学计算机科学学院, 安徽 芜湖 241000 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11401009; 11326062). |
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| 摘 要： | As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a∈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.
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| 关 键 词： | $r$-clean环 弱clean环 弱$r$-clean环 正则环 |
| 收稿时间： | 2016/10/13 0:00:00 |
| 修稿时间： | 2017/5/17 0:00:00 |
On Weakly $r$-Clean Rings |
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| Hanpeng GAO and Xiaobin YIN.On Weakly $r$-Clean Rings[J].Journal of Mathematical Research with Applications,2017,37(5):543-549. |
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| Authors: | Hanpeng GAO and Xiaobin YIN |
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| Institution: | Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China and Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China |
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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. |
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| Keywords: | $r$-clean rings weakly clean rings weakly $r$-clean rings regular rings |
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