Dedekind domains and Dedekind modules (Q2826322)
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scientific article; zbMATH DE number 6639510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dedekind domains and Dedekind modules |
scientific article; zbMATH DE number 6639510 |
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14 October 2016
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Dedekind modules
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uniform modules
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Dedekind domains
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Dedekind domains and Dedekind modules (English)
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If \(R\) is a commutative ring, then an \(R\)-module is said to be a Dedekind module if all its non-zero submodules are invertible [\textit{A. G. Naoum} and \textit{F. H. Al-Alwan}, Commun. Algebra 24, No. 2, 397--412 (1996; Zbl 0858.13008)]. The authors show that an integral domain \(R\) is Dedekind if and only if every torsion-free finitely generated uniform \(R\)-module is a Dedekind module.
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