Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.11303 |
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Inhaltsangabe:
- 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.