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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we give a detailed description of such modules when $G$ is periodic Abelian and the spectrum of $D$ is infinite.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $D$ be a Dedekind domain and $G$ be a periodic Abelian-by-finite group.
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Key Findings & Data:In this paper we study $DG$-modules in which every factor-module, apart from the trivial one, is $DG$-Artinian.
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Conclusion & Impact:Finally, we give a detailed description of such modules when $G$ is periodic Abelian and the spectrum of $D$ is infinite.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Almost Artinian module · Dedekind domain
Abstract
Let $D$ be a Dedekind domain and $G$ be a periodic Abelian-by-finite group. In this paper we study $DG$-modules in which every factor-module, apart from the trivial one, is $DG$-Artinian. In particular we prove that such modules cannot be $D$-periodic and that $G$ must be subject to some restrictions. Finally, we give a detailed description of such modules when $G$ is periodic Abelian and the spectrum of $D$ is infinite.
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Cite This Article
KURDACHENKO, L. A., TROMBETTI, M. (2022). Just non-Artinian modules over some group rings. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1242–1254. https://ajindex.com/articles/608140