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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 6

Zariski subspace topologies on ideals

Ortaç Öneş
Mustafa Alkan
Pages
1667–1674
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

We also give a characterization for the radical of an ideal in $R$ by using topological properties.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we show how there are tight relationships between algebraic properties of a commutative ring $R$ and topological properties of open subsets of Zariski topology on the prime spectrum of $R$.
📊
Key Findings & Data:We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible.
💡
Conclusion & Impact:We also give a characterization for the radical of an ideal in $R$ by using topological properties.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:prime ideal · radical ideal · Zariski topology

Abstract

In this paper, we show how there are tight relationships between algebraic properties of a commutative ring $R$ and topological properties of open subsets of Zariski topology on the prime spectrum of $R$. We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible. We also give a characterization for the radical of an ideal in $R$ by using topological properties.

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Cite This Article

Öneş, O., Alkan, M. (2022). Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1667–1674. https://ajindex.com/articles/529738

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