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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 3

D-Extending Modules

Yılmaz DURĞUN
Pages
914–920
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

The structure of a ring over which d-closed submodules of every module are direct summand (respectively, closed, pure) is studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A submodule $N$ of a module $M$ is called d-closed if $M/N$ has a zero socle.
📊
Key Findings & Data:D-closed submodules are similar concept to s-closed submodules, which are defined through nonsingular modules by Goodearl.
💡
Conclusion & Impact:The structure of a ring over which d-closed submodules of every module are direct summand (respectively, closed, pure) is studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:D-extending modules · d-closed submodules · semiartinian modules

Abstract

A submodule $N$ of a module $M$ is called d-closed if $M/N$ has a zero socle. D-closed submodules are similar concept to s-closed submodules, which are defined through nonsingular modules by Goodearl. In this article we deal with modules with the property that all d-closed submodules are direct summands (respectively, closed, pure). The structure of a ring over which d-closed submodules of every module are direct summand (respectively, closed, pure) is studied.

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Cite This Article

DURĞUN, Y. (2022). D-Extending Modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 3, 914–920. https://ajindex.com/articles/529626

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