数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 645-651.doi: 10.1016/S0252-9602(12)60045-9

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ON ALMOST PRIME SUBMODULES

Hani A. Khashan   

  1. Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
  • 收稿日期:2009-10-26 修回日期:2011-03-20 出版日期:2012-03-20 发布日期:2012-03-20

ON ALMOST PRIME SUBMODULES

Hani A. Khashan   

  1. Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
  • Received:2009-10-26 Revised:2011-03-20 Online:2012-03-20 Published:2012-03-20

摘要:

In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules.

关键词: Prime submodules, weakly prime submodules, almost prime submodules, multiplication modules

Abstract:

In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules.

Key words: Prime submodules, weakly prime submodules, almost prime submodules, multiplication modules

中图分类号: 

  • 13C13