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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 1

On QF rings and artinian principal ideal rings

Alejandro ALVARADO-GARCİA
César CEJUDO-CASTİLLA
Hugo Alberto RİNCONMEJİA
Ivan Fernando VİLCHİS -MONTALVO
Manuel Gerardo ZORRİLLA- NORİEGA
Pages
67–74
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we obtain characterizations of left artinian and left coartinian rings.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work we give sufficient conditions for a ring $R$ to be quasi-Frobenius, such as $R$ being left artinian and the class of injective cogenerators of $R$-Mod being closed under projective covers.
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Key Findings & Data:We prove that $R$ is a division ring if and only if $R$ is a domain and the class of left free $R$-modules is closed under injective hulls.
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Conclusion & Impact:Finally, we obtain characterizations of left artinian and left coartinian rings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:left artinian ring · artinian principal ideal ring · conoetherian ring

Abstract

In this work we give sufficient conditions for a ring $R$ to be quasi-Frobenius, such as $R$ being left artinian and the class of injective cogenerators of $R$-Mod being closed under projective covers. We prove that $R$ is a division ring if and only if $R$ is a domain and the class of left free $R$-modules is closed under injective hulls. We obtain some characterizations of artinian principal ideal rings. We characterize the rings for which left cyclic modules coincide with left cocyclic $R$-modules. Finally, we obtain characterizations of left artinian and left coartinian rings.

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Cite This Article

ALVARADO-GARCİA, A., CEJUDO-CASTİLLA, C., RİNCONMEJİA, H. A., -MONTALVO, I. F. V., NORİEGA, M. G. Z. (2022). On QF rings and artinian principal ideal rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 1, 67–74. https://ajindex.com/articles/530154

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References (5)

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