End á´ª -Prime Submodules
Let R be a commutative ring with identity and M an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x ïƒ...
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| Format: | Article |
| Language: | English |
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University of Baghdad
2017-03-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/115 |
| _version_ | 1811308153390759936 |
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| author | Nuhad S. AL-Mothafar Adwia J. Abdil -Khalik |
| author_facet | Nuhad S. AL-Mothafar Adwia J. Abdil -Khalik |
| author_sort | Nuhad S. AL-Mothafar |
| collection | DOAJ |
| description |
Let R be a commutative ring with identity and M an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x  P + ï¹(P) or ï¡(M) ïƒ P + ï¹(P). Some of the properties of this concept will be investigated. Some characterizations of end-ï¹-prime submodules will be given, and we show that under some assumtions prime submodules and end-ï¹-prime submodules are coincide.
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| first_indexed | 2024-04-13T09:18:01Z |
| format | Article |
| id | doaj.art-a39c83089fc44e9a847aab353d76ee1a |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-13T09:18:01Z |
| publishDate | 2017-03-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-a39c83089fc44e9a847aab353d76ee1a2022-12-22T02:52:42ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072017-03-01292End á´ª -Prime SubmodulesNuhad S. AL-MothafarAdwia J. Abdil -Khalik Let R be a commutative ring with identity and M an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x  P + ï¹(P) or ï¡(M) ïƒ P + ï¹(P). Some of the properties of this concept will be investigated. Some characterizations of end-ï¹-prime submodules will be given, and we show that under some assumtions prime submodules and end-ï¹-prime submodules are coincide. https://jih.uobaghdad.edu.iq/index.php/j/article/view/115Prime submoduleweakly prime submodulesɸ-prime submodules |
| spellingShingle | Nuhad S. AL-Mothafar Adwia J. Abdil -Khalik End ᴪ -Prime Submodules Ibn Al-Haitham Journal for Pure and Applied Sciences Prime submodule weakly prime submodules ɸ-prime submodules |
| title | End á´ª -Prime Submodules |
| title_full | End á´ª -Prime Submodules |
| title_fullStr | End á´ª -Prime Submodules |
| title_full_unstemmed | End á´ª -Prime Submodules |
| title_short | End á´ª -Prime Submodules |
| title_sort | end a´ª prime submodules |
| topic | Prime submodule weakly prime submodules ɸ-prime submodules |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/115 |
| work_keys_str_mv | AT nuhadsalmothafar endaaprimesubmodules AT adwiajabdilkhalik endaaprimesubmodules |