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A Note on an R-Modules with Nearly Pure Intersection Property | ||
| Journal of Al-Nahrain University - Science | ||
| Article 1, Volume 16, Issue 1, 2013, Pages 171-175 | ||
| Author | ||
| Nuhad S. Al-Mothafar | ||
| Abstract | ||
| Let R be a commutative ring with identity and let M be a left R–module. A submoduleN of an R-module M is said to be nearly pure of M (abbreviated by N- pure), if N⋂IM=IN+J(M)⋂(N⋂IM), for each ideal Iof R; where J(M) is the Jacobson radical of M. The main purpose of this paper is to introduce the concept of modules with the Nearly Pure intersection property, andwe show that if M=A⊕B, has the NPIP and f:A→B is an R-homomorphism for any N – pure submodules A and B, then kernel f is N-pure. | ||
| Keywords | ||
| Pure submodule; Nearly Pure submodule; module with the Nearly Pureintersection property | ||
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