On MLGP- Rings

Abstract

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 am = am b ( am = b am) . 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: 1- Let R be a local ,MLGP and SXM ring. Then: (a) J (R) = 0. (b) If R is NJ-ring. Then r(am) is a direct sum and for all ∈ R, m ∈ Z+. 2- Let R be a local, SXM and NJ-ring . Then R is strongly π-regular if and only if R i LGP.

Keywords

• nj rings
• sxm rings
• local strongly regular rings
• pure ideals