Some Results on Pure Submodules Relative to Submodule
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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essentia...
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University of Baghdad, College of Science for Women
2015-12-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2132 |
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| author | Baghdad Science Journal |
| author_facet | Baghdad Science Journal |
| author_sort | Baghdad Science Journal |
| collection | DOAJ |
| description | 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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending. |
| format | Article |
| id | doaj-art-d3ec745d70514fdbacf7070b95905bd3 |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-d3ec745d70514fdbacf7070b95905bd32025-08-20T02:51:27ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862015-12-0112410.21123/bsj.12.4.833-837Some Results on Pure Submodules Relative to SubmoduleBaghdad Science JournalLet 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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2132T-pure submodule, T-pure essential submodule and T-pure closed submodule. |
| spellingShingle | Baghdad Science Journal Some Results on Pure Submodules Relative to Submodule مجلة بغداد للعلوم T-pure submodule, T-pure essential submodule and T-pure closed submodule. |
| title | Some Results on Pure Submodules Relative to Submodule |
| title_full | Some Results on Pure Submodules Relative to Submodule |
| title_fullStr | Some Results on Pure Submodules Relative to Submodule |
| title_full_unstemmed | Some Results on Pure Submodules Relative to Submodule |
| title_short | Some Results on Pure Submodules Relative to Submodule |
| title_sort | some results on pure submodules relative to submodule |
| topic | T-pure submodule, T-pure essential submodule and T-pure closed submodule. |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2132 |
| work_keys_str_mv | AT baghdadsciencejournal someresultsonpuresubmodulesrelativetosubmodule |