On Strongly $m$-$\Delta$-clean ring

Abstract

Motivated by the recent study of strongly $\Delta$-clean rings, we introduce and study strongly $m$-$\Delta$-clean rings. We establish their fundamental properties and characterize strongly $m$-$\Delta$-clean rings via lifting $m$-potent elements modulo $\Delta (R)$. We prove that every $m$-$\Delta$-clean ring is clean and that the factor ring of a strongly $m$-$\Delta$-clean ring modulo its Jacobson radical is reduced. Finally, we investigate corner rings, Morita context rings, and the relationships of these rings with $\Delta$-clean, local, semipotent, and strongly $m$-nil clean rings.