On П-pure ideals

Abstract EN

As a generalization of right pure ideals, we introduce the notion of right П–pure ideals.

A right ideal I of R is said to be П – pure, if for every a ε I there exists b ε I and a positive integer n such that an ≠ 0 and an b = an.

In this paper, we give some characterizations and properties of П–pure ideals and it is proved that : If every principal right ideal of a ring R is П–pure then, a).

L (an) = L (an + 1) for every a ε R and for some positive integer n. b).

R is directly finite ring. c).

R is strongly П–regular ring.