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...
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| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| 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| _version_ | 1856543051678220288 |
|---|---|
| author | Hamid, M. F. |
| author_facet | Hamid, M. F. |
| author_sort | Hamid, M. F. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-07-19T08:39:30Z |
| description | 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. |
| first_indexed | 2025-12-02T15:50:01Z |
| format | Article |
| id | admjournalluguniveduua-article-1209 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:50:01Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-12092021-07-19T08:39:30Z On (co)pure Baer injective modules Hamid, M. F. \(\mathcal{Q}\)-copure submodule, \(\mathcal{Q}\)-copure Baer injective module, pure Baer injective module 16D50 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. Lugansk National Taras Shevchenko University 2021-07-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1209 10.12958/adm1209 Algebra and Discrete Mathematics; Vol 31, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1209/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1209/387 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | \(\mathcal{Q}\)-copure submodule \(\mathcal{Q}\)-copure Baer injective module pure Baer injective module 16D50 Hamid, M. F. On (co)pure Baer injective modules |
| title | On (co)pure Baer injective modules |
| title_full | On (co)pure Baer injective modules |
| title_fullStr | On (co)pure Baer injective modules |
| title_full_unstemmed | On (co)pure Baer injective modules |
| title_short | On (co)pure Baer injective modules |
| title_sort | on (co)pure baer injective modules |
| topic | \(\mathcal{Q}\)-copure submodule \(\mathcal{Q}\)-copure Baer injective module pure Baer injective module 16D50 |
| topic_facet | \(\mathcal{Q}\)-copure submodule \(\mathcal{Q}\)-copure Baer injective module pure Baer injective module 16D50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1209 |
| work_keys_str_mv | AT hamidmf oncopurebaerinjectivemodules |