On П – Pure Ideals

Abstract

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.

Keywords

• pure
• strongly regular
• п – ring