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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| Datum: | 2021 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2021
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2021-07-19T08:39:30Z |
| collection |
OJS |
| language |
English |
| topic |
\(\mathcal{Q}\)-copure submodule \(\mathcal{Q}\)-copure Baer injective module pure Baer injective module 16D50 |
| 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 |
| topic_facet |
\(\mathcal{Q}\)-copure submodule \(\mathcal{Q}\)-copure Baer injective module pure Baer injective module 16D50 |
| format |
Article |
| author |
Hamid, M. F. |
| author_facet |
Hamid, M. F. |
| author_sort |
Hamid, M. F. |
| title |
On (co)pure Baer injective modules |
| title_short |
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_sort |
on (co)pure baer injective modules |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1209 |
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AT hamidmf oncopurebaerinjectivemodules |
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2025-07-17T10:31:54Z |
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2025-07-17T10:31:54Z |
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