On The Regularity Of Rings

In this paper,the regularity of rings is mainly investigated.In section one,we list some conceptions and lemmas for later use.In section two,the regularity of MERT-rings under certain conditions is discussed,some results that MERT-ring is regular ring are obtained.In section three.the conception of MLW-rings and MELW-rings are defined and some new results on regularity related to SF-rings are given,the connections between MLW-rings and quasi-duo rings are also discussed.In section four,the regularity of MLW-rings and MELW-rings characterized by the GP-injectivity of their modules are studied respectively,which generalized the corresponding results of [4] and [14].