Nilpotent elements and reduced rings

Authors : Junchao WEI, Libin LI

Pages : 341-353

View : 12 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we show the following results: insert ignore into journalissuearticles values(1); R is a min-leftsemicentral ring if and only if eRinsert ignore into journalissuearticles values(1-e);Re=0 for all e \in MElinsert ignore into journalissuearticles values(R);; insert ignore into journalissuearticles values(2); Quasi-normal rings, NI rings and weakly reversible rings are all min-leftsemicentral ring; insert ignore into journalissuearticles values(3); R is left MC2 ring if and only if aRe=0 implies eRa=0 for all e \in MElinsert ignore into journalissuearticles values(R); and a \in R if and only if every projective simple left R-module is MUP-injective; insert ignore into journalissuearticles values(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; insert ignore into journalissuearticles values(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.
Keywords : Min leftsemicentral rings, quasi normal rings NCI rings, weakly reversible rings, left MC2 rings, directly finite rings, regular rings