حول الحلقات من النمط MLGP

Abstract EN

An ideal K of a ring R is called right (left) generalized pure (GP-ideal)if for every a∈K, there exists m∈Z^+, and b∈K such that a^m=a^m b ( a^m=b a^m ) .

A ring R is called MLGP- ring if every right maximal ideal is left GP- ideal .

In this paper have been studied some new properties of MLGP- rings and the relation between this rings and strongly π- regular rings some of the main result of the present work are as follows: Let R be a local , MLGP and SXM ring .

Then : J(R)=0 .

If R is NJ- ring .

Then r(a^m) is a direct sum and for all ∈R , m∈Z^+ .

- Let R be a local , SXM and NJ- ring .

Then R is strongly π- regular if and only if R i LGP .