On Strongly $m$-$Δ$-clean ring

Abstract

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.