For Some Results of Semisecond Submodules
Let ℛ be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ. In this work, we introduce the concept of semisecond submodule and confer numero...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2018-11-01
|
| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/1999 |
| _version_ | 1818270491863941120 |
|---|---|
| author | Rasha I. Khalaf |
| author_facet | Rasha I. Khalaf |
| author_sort | Rasha I. Khalaf |
| collection | DOAJ |
| description |
Let ℛ be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ.
In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.
|
| first_indexed | 2024-12-12T21:11:08Z |
| format | Article |
| id | doaj.art-81d475e3df2c4c0d83b602207bb21a87 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-12-12T21:11:08Z |
| publishDate | 2018-11-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-81d475e3df2c4c0d83b602207bb21a872022-12-22T00:11:54ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072018-11-0131310.30526/31.3.1999For Some Results of Semisecond SubmodulesRasha I. Khalaf Let ℛ be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ. In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ. https://jih.uobaghdad.edu.iq/index.php/j/article/view/1999Semisecond submodules, second submodules, secondary submodules. |
| spellingShingle | Rasha I. Khalaf For Some Results of Semisecond Submodules Ibn Al-Haitham Journal for Pure and Applied Sciences Semisecond submodules, second submodules, secondary submodules. |
| title | For Some Results of Semisecond Submodules |
| title_full | For Some Results of Semisecond Submodules |
| title_fullStr | For Some Results of Semisecond Submodules |
| title_full_unstemmed | For Some Results of Semisecond Submodules |
| title_short | For Some Results of Semisecond Submodules |
| title_sort | for some results of semisecond submodules |
| topic | Semisecond submodules, second submodules, secondary submodules. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/1999 |
| work_keys_str_mv | AT rashaikhalaf forsomeresultsofsemisecondsubmodules |