Essentially Retractable Modules Relative To A Submodule And Some Generalizations
In this paper, we define a new notion namely essentially retractable module relative to a submodule also, a new generalizations of compressible modules relative to a submodule are introduced where a module is called compressible module relative to a submodule of if for all non-zero submodule of ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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College of Education, Al-Iraqia University
2021-07-01
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| Series: | Iraqi Journal for Computer Science and Mathematics |
| Subjects: | |
| Online Access: | https://journal.esj.edu.iq/index.php/IJCM/article/view/22 |
| _version_ | 1797647572718845952 |
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| author | shukur Al-Aeashi Fatimah Hussein Al-Bakaa |
| author_facet | shukur Al-Aeashi Fatimah Hussein Al-Bakaa |
| author_sort | shukur Al-Aeashi |
| collection | DOAJ |
| description |
In this paper, we define a new notion namely essentially retractable module relative to a submodule also, a new generalizations of compressible modules relative to a submodule are introduced where a module is called compressible module relative to a submodule of if for all non-zero submodule of such that contains , there exists a monomorphism . Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. Also, we introduce another generalization of retractable module which is called small kernel retractable module.
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| first_indexed | 2024-03-11T15:18:29Z |
| format | Article |
| id | doaj.art-b730e9c710984de083b5fa09541dd2f8 |
| institution | Directory Open Access Journal |
| issn | 2958-0544 2788-7421 |
| language | English |
| last_indexed | 2024-03-11T15:18:29Z |
| publishDate | 2021-07-01 |
| publisher | College of Education, Al-Iraqia University |
| record_format | Article |
| series | Iraqi Journal for Computer Science and Mathematics |
| spelling | doaj.art-b730e9c710984de083b5fa09541dd2f82023-10-29T06:16:28ZengCollege of Education, Al-Iraqia UniversityIraqi Journal for Computer Science and Mathematics2958-05442788-74212021-07-012210.52866/ijcsm.2021.02.02.00115Essentially Retractable Modules Relative To A Submodule And Some Generalizationsshukur Al-Aeashi0Fatimah Hussein Al-Bakaa1Department Of Mathematics, College of Education, University Of Kufa, Najaf, IraqDepartment Of Mathematics, College Of Computer Science And Mathematics, University Of Kufa, Najaf, Iraq In this paper, we define a new notion namely essentially retractable module relative to a submodule also, a new generalizations of compressible modules relative to a submodule are introduced where a module is called compressible module relative to a submodule of if for all non-zero submodule of such that contains , there exists a monomorphism . Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. Also, we introduce another generalization of retractable module which is called small kernel retractable module. https://journal.esj.edu.iq/index.php/IJCM/article/view/22Compressible module relative to a submoduleRetractable module relative to a submoduleEssentially retractable module relative to a submoduleSmall kernel retractable module |
| spellingShingle | shukur Al-Aeashi Fatimah Hussein Al-Bakaa Essentially Retractable Modules Relative To A Submodule And Some Generalizations Iraqi Journal for Computer Science and Mathematics Compressible module relative to a submodule Retractable module relative to a submodule Essentially retractable module relative to a submodule Small kernel retractable module |
| title | Essentially Retractable Modules Relative To A Submodule And Some Generalizations |
| title_full | Essentially Retractable Modules Relative To A Submodule And Some Generalizations |
| title_fullStr | Essentially Retractable Modules Relative To A Submodule And Some Generalizations |
| title_full_unstemmed | Essentially Retractable Modules Relative To A Submodule And Some Generalizations |
| title_short | Essentially Retractable Modules Relative To A Submodule And Some Generalizations |
| title_sort | essentially retractable modules relative to a submodule and some generalizations |
| topic | Compressible module relative to a submodule Retractable module relative to a submodule Essentially retractable module relative to a submodule Small kernel retractable module |
| url | https://journal.esj.edu.iq/index.php/IJCM/article/view/22 |
| work_keys_str_mv | AT shukuralaeashi essentiallyretractablemodulesrelativetoasubmoduleandsomegeneralizations AT fatimahhusseinalbakaa essentiallyretractablemodulesrelativetoasubmoduleandsomegeneralizations |