On MP-Rings

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.