On (co)pure Baer injective modules
For a given class of \(R\)-modules \(\mathcal{Q}\), a module \(M\) is called \(\mathcal{Q}\)-copure Baer injective if any map from a \(\mathcal{Q}\)-copure left ideal of \(R\) into \(M\) can be extended to a map from \(R\) into \(M\). Depending on the class \(\mathcal{Q}\), this concept is both a du...
Збережено в:
| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1209 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | For a given class of \(R\)-modules \(\mathcal{Q}\), a module \(M\) is called \(\mathcal{Q}\)-copure Baer injective if any map from a \(\mathcal{Q}\)-copure left ideal of \(R\) into \(M\) can be extended to a map from \(R\) into \(M\). Depending on the class \(\mathcal{Q}\), this concept is both a dualization and a generalization of pure Baer injectivity. We show that every module can be embedded as \(\mathcal{Q}\)-copure submodule of a \(\mathcal{Q}\)-copure Baer injective module. Certain types of rings are characterized using properties of \(\mathcal{Q}\)-copure Baer injective modules. For example a ring \(R\) is \(\mathcal{Q}\)-coregular if and only if every \(\mathcal{Q}\)-copure Baer injective \(R\)-module is injective. |
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