Abstract In this article, we continue the study of strongly m-clean ring which we introduced in the paper “On m-clean and strongly m-clean rings” (Purkait et al. 2020). Mainly, we characterize strongly m-clean ring in terms of m-semiperfect ring. For that, we introduce the notion of m-semiperfect ring and establish some results on this ring. We prove that under certain conditions a ring is m-semiperfect if and only if it is strongly m-clean and orthogonally m-finite.

中文翻译：

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关于强 m-clean 环和 m-semiperfect 环

摘要 在本文中，我们继续研究我们在论文“On m-clean and strong m-clean ring”（Purkait et al. 2020）中介绍的强 m-clean 环。主要是，我们根据 m-semiperfect 环来表征强 m-clean 环。为此，我们引入了 m-semiperfect 环的概念并在该环上建立了一些结果。我们证明在某些条件下，一个环是 m-半完美的当且仅当它是强 m-clean 和正交 m-有限的。