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Notes on Approximately Pure Submodules | ||
| Baghdad Science Journal | ||
| Article 1, Volume 10, Issue 4, 2013, Pages 1269-1272 | ||
| Author | ||
| Zahraa A. Mohammed | ||
| Abstract | ||
| Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending. | ||
| Keywords | ||
| Approximately pure submodule; approximately pure essential submodule and approximately pure closedsubmodule | ||
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