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| 摘要: |
| 本文研究了元素的potent指数和伪clean环,给出了一些伪clean环的性质的例子,证明了Zm(2 ≤ m ∈ Z)是伪clean环以及伪clean环是clean环.此外，本文也证明了伪clean环是直有限的且有稳定秩一. |
| 关键词: clean环 强J-clean环 伪clean环 potent元 |
| DOI： |
| 分类号:O153.3 |
| 基金项目: |
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| ON POTENT ELEMENTS AND PSEUDO CLEAN RINGS |
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DING Yan,GAO Han-peng,LIU Xin-yi,YAN Zi-yi,ZHANG Ting
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| Abstract: |
| In this paper, potent index of an element and pseudo clean rings are considered. Some properties and examples of pseudo clean rings are given. We also show that Zm is pseudo clean for every 2 ≤ m ∈ Z and pseudo clean rings are clean. Furthermore, we prove pseudo clean rings are directly finite and have stable range one. |
| Key words: clean rings strongly J-clean rings pseudo clean rings potent elements |
