Notes on Approximately Pure Submodules
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...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2013-12-01
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| Series: | Baghdad Science Journal |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2839 |
| Summary: | 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. |
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| ISSN: | 2078-8665 2411-7986 |