关于强clean环理论完备性的一个注记
A note on completeness in the theory of strongly clean rings
摘要：
许多作者研究了环扩张下的强清洁性。本文证明了：如果$R$是关于理想$I$完备的环，且$x$是$R$中的一个元素，且其在$R/I$中的象是强$π$ -正则的，则$x$在$R$中是强clean的.
英文摘要：
Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we prove that if $R$ is a ring which is complete with respect to an ideal $I$ and if $x$ is an element of $R$ whose image in $R/I$ is strongly $π$-regular, then $x$ is strongly clean in $R$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
