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: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
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| Теми: | |
| 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| Резюме: | 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. |
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