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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.11303 |
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| _version_ | 1866917269635858432 |
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| author | Cortés-Izurdiaga, Manuel Estrada, Sergio Fresneda, José Manuel |
| author_facet | Cortés-Izurdiaga, Manuel Estrada, Sergio Fresneda, José Manuel |
| contents | We study the class of rings $R$ for which every direct sum of injective $R$-modules is cotorsion. We call them weakly $Σ$-cotorsion rings. The defining property might be seen as the dual of Chase's characterization of coherence in terms of the flatness of every direct product of projective $R$-modules. More generally, we study rings over which direct sums of injective modules have finite cotorsion dimension and call them weakly $n$-$Σ$-cotorsion rings, as well as rings over which direct sums of cotorsion modules have finite cotorsion dimension (called $n$-$Σ$-cotorsion rings). In the process, we obtain new characterizations of $n$-perfect rings and extend previous results by Guil Asensio and Herzog, and by Šaroch and Šťovíček. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11303 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weakly Sigma-cotorsion rings Cortés-Izurdiaga, Manuel Estrada, Sergio Fresneda, José Manuel Rings and Algebras 16E10, 16D90, 16L30 We study the class of rings $R$ for which every direct sum of injective $R$-modules is cotorsion. We call them weakly $Σ$-cotorsion rings. The defining property might be seen as the dual of Chase's characterization of coherence in terms of the flatness of every direct product of projective $R$-modules. More generally, we study rings over which direct sums of injective modules have finite cotorsion dimension and call them weakly $n$-$Σ$-cotorsion rings, as well as rings over which direct sums of cotorsion modules have finite cotorsion dimension (called $n$-$Σ$-cotorsion rings). In the process, we obtain new characterizations of $n$-perfect rings and extend previous results by Guil Asensio and Herzog, and by Šaroch and Šťovíček. |
| title | Weakly Sigma-cotorsion rings |
| topic | Rings and Algebras 16E10, 16D90, 16L30 |
| url | https://arxiv.org/abs/2602.11303 |