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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Main Authors: Nuhad S. AL-Mothafar, Adwia J. Abdil .Al-Khalik
Format: Article
Language:English
Published: University of Baghdad 2017-03-01
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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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
á´ª-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