In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in ME_l(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 \in ME_l(R) and a \in 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.
Min-leftsemicentral rings, quasi-normal rings. NCI rings, weakly reversible rings, left MC2 rings, directly finite rings, regular rings
WEI, JUNCHAO and LI, LIBIN
"Nilpotent elements and reduced rings,"
Turkish Journal of Mathematics: Vol. 35:
2, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/15