发表机构
Department of Mathematics, Jadavpur University（贾达普大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入强 $m$-Δ-clean 环，刻画其性质并证明 $m$-Δ-clean 环是 clean 环、其 Jacobson 根的因子环既约，还探究了相关环类的关系。
AI 中文摘要
受近期强 Δ-clean 环研究的启发，本文引入并研究强 $m$-Δ-clean 环，确立其基本性质，并通过模 Δ(R) 提升 $m$-幂等元来刻画强 $m$-Δ-clean 环。证明每个 $m$-Δ-clean 环都是 clean 环，且强 $m$-Δ-clean 环模其 Jacobson 根的因子环是既约环。最后研究 corner 环、Morita context 环，以及这些环与 Δ-clean、局部、半幂等、强 $m$-nil clean 环的关系。
英文摘要
Motivated by the recent study of strongly $Δ$-clean rings, we introduce and study strongly $m$-$Δ$-clean rings. We establish their fundamental properties and characterize strongly $m$-$Δ$-clean rings via lifting $m$-potent elements modulo $Δ(R)$. We prove that every $m$-$Δ$-clean ring is clean and that the factor ring of a strongly $m$-$Δ$-clean ring modulo its Jacobson radical is reduced. Finally, we investigate corner rings, Morita context rings, and the relationships of these rings with $Δ$-clean, local, semipotent, and strongly $m$-nil clean rings.
