Extending properties of \(z\)-closed projection invariant submodules
In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between...
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| Дата: | 2025 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543348798521344 |
|---|---|
| author | Yücel, Canan Celep Ayvazoğlu, Yeşim |
| author_facet | Yücel, Canan Celep Ayvazoğlu, Yeşim |
| author_sort | Yücel, Canan Celep |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2025-08-13T10:04:13Z |
| description | In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between the other extending properties. Our focus is the behavior of the \(ZPG\) modules with respect to direct sums and direct summands. We obtain the property is closed under right essential overring and rational hull. |
| first_indexed | 2026-02-08T08:01:48Z |
| format | Article |
| id | admjournalluguniveduua-article-2323 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:48Z |
| publishDate | 2025 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-23232025-08-13T10:04:13Z Extending properties of \(z\)-closed projection invariant submodules Yücel, Canan Celep Ayvazoğlu, Yeşim \(zp\)-submodule, \(z\)-closed submodule, \(PI\)-extending module, \(G\)-extending module, \(CS\)-module 16D50, 16D70 In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between the other extending properties. Our focus is the behavior of the \(ZPG\) modules with respect to direct sums and direct summands. We obtain the property is closed under right essential overring and rational hull. Lugansk National Taras Shevchenko University 2025-08-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323 10.12958/adm2323 Algebra and Discrete Mathematics; Vol 39, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1248 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1302 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1303 Copyright (c) 2025 Algebra and Discrete Mathematics |
| spellingShingle | \(zp\)-submodule \(z\)-closed submodule \(PI\)-extending module \(G\)-extending module \(CS\)-module 16D50 16D70 Yücel, Canan Celep Ayvazoğlu, Yeşim Extending properties of \(z\)-closed projection invariant submodules |
| title | Extending properties of \(z\)-closed projection invariant submodules |
| title_full | Extending properties of \(z\)-closed projection invariant submodules |
| title_fullStr | Extending properties of \(z\)-closed projection invariant submodules |
| title_full_unstemmed | Extending properties of \(z\)-closed projection invariant submodules |
| title_short | Extending properties of \(z\)-closed projection invariant submodules |
| title_sort | extending properties of \(z\)-closed projection invariant submodules |
| topic | \(zp\)-submodule \(z\)-closed submodule \(PI\)-extending module \(G\)-extending module \(CS\)-module 16D50 16D70 |
| topic_facet | \(zp\)-submodule \(z\)-closed submodule \(PI\)-extending module \(G\)-extending module \(CS\)-module 16D50 16D70 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323 |
| work_keys_str_mv | AT yucelcanancelep extendingpropertiesofzclosedprojectioninvariantsubmodules AT ayvazogluyesim extendingpropertiesofzclosedprojectioninvariantsubmodules |