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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, cyclic $c-$injective modules are introduced and investigated.
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Key Findings & Data:It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective.
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Conclusion & Impact:Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$c-$Injective modules · Dedekind domains · right V-rings
Abstract
In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
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Cite This Article
DO, T. V., HOANG, H. D., BAUPRADIST, S. (2017). More characterizations of Dedekind domains and V-rings. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 1, 33–42. https://ajindex.com/articles/723231