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On П – Pure Ideals | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 5, Volume 11, Issue 2, 2014, Pages 83-86 PDF (290.26 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2014.163751 | ||
| Author | ||
| Shaimaa Hatem Ahmad | ||
| Mathematics Department College of Computer Science and Mathematics University of Mosul, Mosul, Iraq | ||
| 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 | ||
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