Keywords : Pure

On П – Pure Ideals

Shaimaa Hatem Ahmad

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 2, Pages 83-86
DOI: 10.33899/csmj.2014.163751

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 Î I there exists b Î 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 Î R and for some  positive integer n .
b). R is directly finite ring.
 c). R is strongly   П – regular ring.