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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

On retractability and its relationships with lattices associated to a ring

Manuel Gerardo Zorrilla-Noriega
Manuel Gerardo Zorrilla Noriega
Rodrigo Domínguez López
Oscar Alberto Garrido Jiménez
Pages
1079–1093
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this work is threefold.
📊
Key Findings & Data:First, we explore some relationships between retractability and some lattices of classes of modules.
💡
Conclusion & Impact:In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:left mod-retractable ring · parainjective module · paraprojective module

Abstract

The purpose of this work is threefold. First, we explore some relationships between retractability and some lattices of classes of modules. Secondly, we weaken the hypothesis of a result of Ohtake characterizing rings over which all radicals are left exact. In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.

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Cite This Article

Zorrilla-Noriega, M. G., Noriega, M. G. Z., López, R. D., Jiménez, O. A. G. (2022). On retractability and its relationships with lattices associated to a ring. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1079–1093. https://ajindex.com/articles/529508

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