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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 4

Commutative graded-$n$-coherent and graded valuation rings

Anass Assarrar(University S.M. Ben Abdellah Fez)0000-0002-8877-9287
Najib Mahdou(University S.M. Ben Abdellah Fez)0000-0001-6353-1114
Ünsal Tekir(MARMARA UNIVERSITY)0000-0003-0739-1449
Suat Koç(MARMARA UNIVERSITY)0000-0003-1622-786X
Pages
—
Publication Date
2022-08-01
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AI Summary & Key Takeaways

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

In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$.
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Key Findings & Data:For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced.
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Conclusion & Impact:In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:coherent rings and modules · n-coherent rings and modules · graded modules and rings

Abstract

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$. For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced. In this paper many results are generalized from $n$-coherent rings to graded-$n$-coherent rings. In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

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Cite This Article

Assarrar, A., Mahdou, N., Tekir, Ü., Koç, S. (2022). Commutative graded-$n$-coherent and graded valuation rings. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 4. https://doi.org/10.15672/hujms.947574

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