Rings whose mininjective modules are injective
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915253368913920 |
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| author | Alagöz, Yusuf Benli-Göral, Sinem Büyükaşık, Engin Rozas, Juan Ramón García Oyonarte, Luis |
| author_facet | Alagöz, Yusuf Benli-Göral, Sinem Büyükaşık, Engin Rozas, Juan Ramón García Oyonarte, Luis |
| contents | The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian rings for which every min-flat module is projective and we study this characterization in the cases when the ring is Kasch, commutative and when it is quasi-Frobenius. We also treat the case of $n\times n$ upper triangular matrix rings, proving that their mininjective modules are injective if and only if $n=2$.
We use the developed machinery to find a new type of examples of indigent modules (those whose subinjectivity domain contains only the injective modules), whose existence is known, so far, only in some rather restricted situations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings whose mininjective modules are injective Alagöz, Yusuf Benli-Göral, Sinem Büyükaşık, Engin Rozas, Juan Ramón García Oyonarte, Luis Rings and Algebras 16D10, 16D50, 16E30 The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian rings for which every min-flat module is projective and we study this characterization in the cases when the ring is Kasch, commutative and when it is quasi-Frobenius. We also treat the case of $n\times n$ upper triangular matrix rings, proving that their mininjective modules are injective if and only if $n=2$. We use the developed machinery to find a new type of examples of indigent modules (those whose subinjectivity domain contains only the injective modules), whose existence is known, so far, only in some rather restricted situations. |
| title | Rings whose mininjective modules are injective |
| topic | Rings and Algebras 16D10, 16D50, 16E30 |
| url | https://arxiv.org/abs/2504.15775 |