On П – Pure Ideals
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 a<sup>n</sup> ≠ 0 and a<sup>n </sup>b = a<sup>n</sup>...
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| Format: | Article |
| Language: | Arabic |
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Mosul University
2014-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_163751_d6d1b144928ba973a7890f7a50df566a.pdf |
| Summary: | 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 a<sup>n</sup> ≠ 0 and a<sup>n </sup>b = a<sup>n</sup>. 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 (a<sup>n</sup>) = L (a<sup>n+1</sup><strong>) </strong>for every a Î R and for some positive integer n .
b). R is directly finite ring.
c). R is strongly П – regular ring.
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| ISSN: | 1815-4816 2311-7990 |