á´ª-Prime Submodules
Let R be a commutative ring with identity and M be 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 ï¹-prime if for each r  R and x  M, if rx  P, then either x  P + ï¹(P) o...
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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/117 |
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author | Nuhad S. AL-Mothafar Adwia J. Abdil .Al-Khalik |
author_facet | Nuhad S. AL-Mothafar Adwia J. Abdil .Al-Khalik |
author_sort | Nuhad S. AL-Mothafar |
collection | DOAJ |
description |
Let R be a commutative ring with identity and M be 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 ï¹-prime if for each r  R and x  M, if rx  P, then either x  P + ï¹(P) or r M ïƒ P + ï¹(P) . Some of the properties of this concept will be investigated. Some characterizations of ï¹-prime submodules will be given, and we show that under some assumptions prime submodules and ï¹-prime submodules are coincide.
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first_indexed | 2024-12-12T00:25:15Z |
format | Article |
id | doaj.art-58fb4a60d06647189236b2a1cfd8eb16 |
institution | Directory Open Access Journal |
issn | 1609-4042 2521-3407 |
language | English |
last_indexed | 2024-12-12T00:25:15Z |
publishDate | 2017-03-01 |
publisher | University of Baghdad |
record_format | Article |
series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
spelling | doaj.art-58fb4a60d06647189236b2a1cfd8eb162022-12-22T00:44:38ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072017-03-01292á´ª-Prime SubmodulesNuhad S. AL-MothafarAdwia J. Abdil .Al-Khalik Let R be a commutative ring with identity and M be 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 ï¹-prime if for each r  R and x  M, if rx  P, then either x  P + ï¹(P) or r M ïƒ P + ï¹(P) . Some of the properties of this concept will be investigated. Some characterizations of ï¹-prime submodules will be given, and we show that under some assumptions prime submodules and ï¹-prime submodules are coincide. https://jih.uobaghdad.edu.iq/index.php/j/article/view/117Prime submoduleweakly prime submodulesɸ-prime submodules |
spellingShingle | Nuhad S. AL-Mothafar Adwia J. Abdil .Al-Khalik ᴪ-Prime Submodules Ibn Al-Haitham Journal for Pure and Applied Sciences Prime submodule weakly prime submodules ɸ-prime submodules |
title | á´ª-Prime Submodules |
title_full | á´ª-Prime Submodules |
title_fullStr | á´ª-Prime Submodules |
title_full_unstemmed | á´ª-Prime Submodules |
title_short | á´ª-Prime Submodules |
title_sort | a´ª prime submodules |
topic | Prime submodule weakly prime submodules ɸ-prime submodules |
url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/117 |
work_keys_str_mv | AT nuhadsalmothafar aaprimesubmodules AT adwiajabdilalkhalik aaprimesubmodules |