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Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 3

UC modules with respect to a torsion theory

Mustafa ALKAN
Seçil ÇEKEN
Pages
376–385
Publication Date
2022-11-04
DOI
—
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AI Summary & Key Takeaways

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

We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of t-closed submodule which was studied in [2].
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Key Findings & Data:We compare UC and t-UC modules and examine the relationships between them.
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Conclusion & Impact:We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hereditary torsion theory · t-closed submodule · UC module

Abstract

In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of t-closed submodule which was studied in [2]. We compare UC and t-UC modules and examine the relationships between them. We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.

Özet

In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of t-closed submodule which was studied in [2]. We compare UC and t-UC modules and examine the relationships between them. We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.

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Cite This Article

ALKAN, M., ÇEKEN, S. (2022). UC modules with respect to a torsion theory. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 3, 376–385. https://ajindex.com/articles/608396

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