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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this note some properties of coatomic modules are studied and it is shown that the following are equivalent for a module M over a Dedekind domain R: (1) M is a coatomic module. (2) Every submodule of M is coatomic. (3) M/L is reduced for every submodule L of M.
📌 3 Key Takeaways
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Objective & Hypothesis:Let R be a ring with identity and M a unital right R-module.
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Key Findings & Data:Let R be a ring with identity and M a unital right R-module.
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Conclusion & Impact:In this note some properties of coatomic modules are studied and it is shown that the following are equivalent for a module M over a Dedekind domain R: (1) M is a coatomic module. (2) Every submodule of M is coatomic. (3) M/L is reduced for every submodule L of M.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let R be a ring with identity and M a unital right R-module. In this note some properties of coatomic modules are studied and it is shown that the following are equivalent for a module M over a Dedekind domain R: (1) M is a coatomic module. (2) Every submodule of M is coatomic. (3) M/L is reduced for every submodule L of M.
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Cite This Article
GÜNGÖROĞLU, G., HARMANCI, A. (2022). Coatomic modules over Dedekind domains. Hacettepe Bulletin of Natural Sciences and Engineering Series B / Mathematics and Statistics, Cilt: 28 - Sayı:, 25–29. https://ajindex.com/articles/528317