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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Tercan would like to thank him for this reference.
📌 3 Key Takeaways
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Objective & Hypothesis:After the paper [1] was published, the following information about D-extending modules was pointed out by Adnan Tercan.
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Key Findings & Data:A submodule $N$ of $M$ is called exact in $M$ provided $r(M/N)=0$.
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Conclusion & Impact:Tercan would like to thank him for this reference.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:D-extending modules · d-closed submodules · semiartinian modules
Abstract
After the paper [1] was published, the following information about D-extending modules was pointed out by Adnan Tercan. Let $r$ be a left exact preradical in the category of right $R$-modules and let $M$ be a right $R$-module. A submodule $N$ of $M$ is called exact in $M$ provided $r(M/N)=0$. A module $M$ is called an ES-module provided every exact submodule of $M$ is a direct summand of $M$. ES-modules was introduced by A. Tercan in [2]. Since socle is left exact preradical, ES-modules coincide with D-extending modules for $r=Soc$.The author who first noticed the ES-module via personal communication with A. Tercan would like to thank him for this reference.
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Cite This Article
Durgun, Y. (2022). Addendum to "D-extending modules" [Hacet. J. Math. Stat. 49(3), 914-920, 2020]. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1169–1169. https://ajindex.com/articles/529551