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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Some commutative ring extensions defined by almost Bézout condition

Najib Ouled Azaiez(King Faisal University)0000-0002-0082-4611
Moutu Abdou Salam Moutui(King Faisal University)0000-0002-7544-2749
Pages
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Publication Date
2020-02-06
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

As an application of our results, we characterize pairs of rings $(R,T)$, where $R$ arises from a $(T,M,D)$ construction to be an almost Bézout domain.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the almost Bézout property in different commutative ring extensions, namely, in bi-amalgamated algebras and pairs of rings.
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Key Findings & Data:In Section 2, we deal with almost Bézout domains issued from bi-amalgamations.
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Conclusion & Impact:As an application of our results, we characterize pairs of rings $(R,T)$, where $R$ arises from a $(T,M,D)$ construction to be an almost Bézout domain.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bi-amalgamated algebra · almost Bézout domain · pairs of rings

Abstract

In this paper, we study the almost Bézout property in different commutative ring extensions, namely, in bi-amalgamated algebras and pairs of rings. In Section 2, we deal with almost Bézout domains issued from bi-amalgamations. Our results capitalize well known results on amalgamations and pullbacks as well as generate new original class of rings satisfying this property. Section 3 investigates pairs of rings where all intermediate rings are almost Bézout domains. As an application of our results, we characterize pairs of rings $(R,T)$, where $R$ arises from a $(T,M,D)$ construction to be an almost Bézout domain.

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Cite This Article

Azaiez, N. O., Moutui, M. A. S. (2020). Some commutative ring extensions defined by almost Bézout condition. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/hujms.552224

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