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 for all e \in 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 \in MEl(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.

Anahtar Kelimeler:

Min-leftsemicentral rings, quasi-normal rings. NCI rings, weakly reversible rings, left MC2 rings, directly finite rings, regular rings

Nilpotent elements and reduced rings

Keywords:

Min-leftsemicentral rings, quasi-normal rings. NCI rings, weakly reversible rings, left MC2 rings, directly finite rings, regular rings,

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Junchao WEI, Libin LI School of Mathematics, Yangzhou University, Yangzhou, 225002, P. R. China e-mail: jcweiyz@yahoo.com.cn