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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 5

Rings for which every cosingular module is discrete

Yahya Talebi(University of Mazandaran)0000-0003-2311-4628
Ali Reza Moniri Hamzekolaee(University of Mazandaran)0000-0002-2852-7870
Abdullah Harmancı(HACETTEPE UNIVERSITY)0000-0001-5691-933X
Burcu Üngör(ANKARA UNIVERSITY)0000-0001-7659-9185
Pages
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Publication Date
2020-10-06
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AI Summary & Key Takeaways

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⚡ 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.
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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

Talebi, Y., Hamzekolaee, A. R. M., Harmancı, A., Üngör, B. (2020). Rings for which every cosingular module is discrete. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 5. https://doi.org/10.15672/hujms.500759

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