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 |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163751_d6d1b144928ba973a7890f7a50df566a.pdf |
| _version_ | 1811263984196648960 |
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| author | Shaimaa Ahmad |
| author_facet | Shaimaa Ahmad |
| author_sort | Shaimaa Ahmad |
| collection | DOAJ |
| description | 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.
<strong> </strong> |
| first_indexed | 2024-04-12T19:54:59Z |
| format | Article |
| id | doaj.art-ed82bdf854fd4c29bdace99783f0cb2d |
| institution | Directory Open Access Journal |
| issn | 1815-4816 2311-7990 |
| language | Arabic |
| last_indexed | 2024-04-12T19:54:59Z |
| publishDate | 2014-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj.art-ed82bdf854fd4c29bdace99783f0cb2d2022-12-22T03:18:42ZaraMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902014-12-01112838610.33899/csmj.2014.163751163751On П – Pure IdealsShaimaa Ahmad0Mathematics Department College of Computer Science and Mathematics University of Mosul, Mosul, IraqAs 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. <strong> </strong>https://csmj.mosuljournals.com/article_163751_d6d1b144928ba973a7890f7a50df566a.pdfpurestrongly regularп – ring |
| spellingShingle | Shaimaa Ahmad On П – Pure Ideals Al-Rafidain Journal of Computer Sciences and Mathematics pure strongly regular п – ring |
| title | On П – Pure Ideals |
| title_full | On П – Pure Ideals |
| title_fullStr | On П – Pure Ideals |
| title_full_unstemmed | On П – Pure Ideals |
| title_short | On П – Pure Ideals |
| title_sort | on п pure ideals |
| topic | pure strongly regular п – ring |
| url | https://csmj.mosuljournals.com/article_163751_d6d1b144928ba973a7890f7a50df566a.pdf |
| work_keys_str_mv | AT shaimaaahmad onppureideals |