Keywords : NJ Rings


On MLGP- Rings

Raida D. mahmood; Ebtehal S. Mageed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2019, Volume 13, Issue 2, Pages 61-66
DOI: 10.33899/csmj.2020.163521

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.