Various properties and characterizations of Dedekind modules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of O(M)M.
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Key Findings & Data:In addition it is proved that the endomorphism ring of a finitely generated torsion free Dedekind module M is a Dedekind domain.
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Conclusion & Impact:Various properties and characterizations of Dedekind modules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dedekind modules and Dedekind domains · Invertible submodules · Duo modules
Abstract
In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of O(M)M. In addition it is proved that the endomorphism ring of a finitely generated torsion free Dedekind module M is a Dedekind domain. Also, we give equivalent condition for Dedekind modules, duo modules and uniform modules. Various properties and characterizations of Dedekind modules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.
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