Keywords : NBF-ring

On MP-Rings

Raida D. Mahmood; Azhar M. Hajo

AL-Rafidain Journal of Computer Sciences and Mathematics, 2020, Volume 14, Issue 1, Pages 35-40
DOI: 10.33899/csmj.2020.164797

An ideal I of a ring R is said to be right (left) Pure if for every  , there is    such that  . A ring R is said to be right (left) MP-ring, if every maximal right (left) ideal of R is a left (right) pure. In this paper have been studied some new properties of MP-rings, there connections with strongly regular rings.
Some of the main result of the present work are as follows:
1- Let R be aright MP-ring, r(a) is a W-ideal for all  then
a- Every essential ideal is a direct summand.  
b- R is strongly regular ring. 
2- Let R be aright MP-ring. If R is right almost abelian left NBF ring, then R is strongly regular.