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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Volume: 48 Issue: 6

Zariski subspace topologies on ideals

Ortaç Öneş(DEPARTMENT OF MATHEMATICS)0000-0001-6777-9192
Mustafa Alkan(DEPARTMENT OF MATHEMATICS)0000-0002-4452-4442
Sayfa
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Yayın Tarihi
2019-12-08
DOI
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We also give a characterization for the radical of an ideal in $R$ by using topological properties.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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 $R$.
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Temel Bulgular & Veri:We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible.
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Sonuç & Katkı:We also give a characterization for the radical of an ideal in $R$ by using topological properties.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Öneş, O., Alkan, M. (2019). Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 6. https://ajindex.com/articles/1402710

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Kaynakça (14)

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