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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 5

Rings for which every cosingular module is discrete

Burcu ÜNGÖR
Yahya TALEBİ
Ali Reza Moniri HAMZEKOLAEE
Abdullah HARMANCI
Pages
1635–1648
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Besides of these, we characterize $CD$-modules with finite hollow dimension.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we introduce the concepts of $CD$-rings and $CD$-modules.
📊
Key Findings & Data:Let $R$ be a ring and $M$ be an $R$-module.
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Conclusion & Impact:Besides of these, we characterize $CD$-modules with finite hollow dimension.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:CD-module · CD-ring · cosingular module

Abstract

In this paper we introduce the concepts of $CD$-rings and $CD$-modules. Let $R$ be a ring and $M$ be an $R$-module. We call $R$ a $CD$-ring in case every cosingular $R$-module is discrete, and $M$ a $CD$-module if every $M$-cosingular $R$-module in $\sigma[M]$ is discrete. If $R$ is a ring such that the class of cosingular $R$-modules is closed under factor modules, then it is proved that $R$ is a $CD$-ring if and only if every cosingular $R$-module is semisimple. The relations of $CD$-rings are investigated with $V$-rings, $GV$-rings, $SC$-rings, and rings with all cosingular $R$-modules projective. If $R$ is a semilocal ring, then it is shown that $R$ is right $CD$ if and only if $R$ is left $SC$ with $Soc(_{R}R)$ essential in $_{R}R$. Also, being a $V$-ring and being a $CD$-ring coincide for local rings. Besides of these, we characterize $CD$-modules with finite hollow dimension.

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Cite This Article

ÜNGÖR, B., TALEBİ, Y., HAMZEKOLAEE, A. R. M., HARMANCI, A. (2022). Rings for which every cosingular module is discrete. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1635–1648. https://ajindex.com/articles/529637

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