Keywords : NJ Rings
AL-Rafidain Journal of Computer Sciences and Mathematics,
2019, Volume 13, Issue 2, Pages 61-66
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.