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

$k$-Congruences and the Zariski topology in semirings

Song-chol Han(Kim Il Sung University)0000-0002-3846-5749
Pages
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Publication Date
2021-06-07
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⚡ TL;DR(Too Long; Didn't Read)

We first prove that the $k$-prime spectrum, i.e. the set of all $k$-prime ideals equipped with the Zariski topology is a spectral space, and then prove that the set of all $k$-prime congruences is homeomorphic to the $k$-prime spectrum with respect to their Zariski topologies.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this paper is to study topological properties of both the set of all $k$-prime ideals and the set of all $k$-prime congruences for any commutative semiring with zero and identity.
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Key Findings & Data:The purpose of this paper is to study topological properties of both the set of all $k$-prime ideals and the set of all $k$-prime congruences for any commutative semiring with zero and identity.
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Conclusion & Impact:We first prove that the $k$-prime spectrum, i.e. the set of all $k$-prime ideals equipped with the Zariski topology is a spectral space, and then prove that the set of all $k$-prime congruences is homeomorphic to the $k$-prime spectrum with respect to their Zariski topologies.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:semiring · ideal · congruence

Abstract

The purpose of this paper is to study topological properties of both the set of all $k$-prime ideals and the set of all $k$-prime congruences for any commutative semiring with zero and identity. We first prove that the $k$-prime spectrum, i.e. the set of all $k$-prime ideals equipped with the Zariski topology is a spectral space, and then prove that the set of all $k$-prime congruences is homeomorphic to the $k$-prime spectrum with respect to their Zariski topologies.

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Cite This Article

Han, S. (2021). $k$-Congruences and the Zariski topology in semirings. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 3. https://doi.org/10.15672/hujms.614688

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