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Potent元及伪clean环

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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.
ON POTENT ELEMENTS AND PSEUDO CLEAN RINGS
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.

clean ringsstrongly J-clean ringspseudo clean ringspotent elements

丁燕、高汉鹏、刘心怡、晏子怡、张婷

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安徽大学数学科学学院,合肥安徽 230601

clean环 强J-clean环 伪clean环 potent元

2025

数学杂志
武汉大学 湖北省数学学会 武汉数学学会

数学杂志

影响因子:0.304
ISSN:0255-7797
年,卷(期):2025.45(1)