Nilpotent elements and reduced rings

In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1 − e)Re =0 forall e element of MEl(R) ; (2) Quasi-normal rings, NI rings and weakly reversible rings are all min- leftsemicentral ring; (3) R is left MC2 ring if and only if aRe = 0 implies eRa =0 for all e element of MEl(R)and a element of R if and only if every projective simple left R-module is MUP -injective; (4) R is reduced if and only if R is n-regular and quasi-normal if and only if R is n-regular and weakly reversible; (5) R is strongly regular if and only if R is regular and quasi-normal if and only if R is regular and weakly reversible.