On П – Pure Ideals

As a generalization of right pure ideals, we introduce the notion of right pure ideals. A right ideal I of R is said to be pure, if for every a I there exists b I and a positive integer n such that an 0 and an b = an. In this paper, we give some characterizations and properties of pure ideals and it is proved that:
If every principal right ideal of a ring R is pure then,
a).L (an) = L (an+1) for every a R and for some positive integer n .
b). R is directly finite ring.
c). R is strongly regular ring.