ON POTENT ELEMENTS AND PSEUDO CLEAN RINGS  

Potent元及伪clean环

作　　者：DING Yan GAO Han-peng LIU Xin-yi YAN Zi-yi ZHANG Ting 丁燕;高汉鹏;刘心怡;晏子怡;张婷(安徽大学数学科学学院,合肥安徽230601)

机构地区：[1]School of Mathematical Sciences,Anhui University,Hefei 230601,China

出　　处：《数学杂志》2025年第1期39-47,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12301041)。

摘　　要：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.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 rings strongly J-clean rings pseudo clean rings potent elements 

分 类 号：O153.3[理学—数学]