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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 3

On the transfer of some $t-$locally properties

Omar Ouzzaouit(Ibn Zohr University)0000-0001-6827-4022
Ali Tamoussit(The Regional Center for Education and Training Professions Souss Massa)0000-0003-1078-0250
Pages
—
Publication Date
2021-06-07
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AI Summary & Key Takeaways

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

A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings of an integral domain $D$.
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Key Findings & Data:We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ are simultaneously $t$-locally P$v$MDs (resp., $t$-locally Krull, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori).
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Conclusion & Impact:A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$t$--Flat overring · ($t$--)Nagata ring · Serre conjecture ring

Abstract

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings of an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ are simultaneously $t$-locally P$v$MDs (resp., $t$-locally Krull, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori). A complete characterization of when a pullback is a $t$-locally P$v$MD (resp., $t$-locally GCD, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori, $t$-locally Mori) is given. As corollaries, we investigate the transfer of some $t$-locally properties among domains of the form $D+XK[X]$, $D+XK[[X]]$ and amalgamated algebras. A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.

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Cite This Article

Ouzzaouit, O., Tamoussit, A. (2021). On the transfer of some $t-$locally properties. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 3. https://doi.org/10.15672/hujms.766283

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