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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Furthermore, two open problems are presented.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $R$ be a ring, $I$ be an ideal of $R$, and $\sqrt{I}$ be a prime radical of $I$.
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Key Findings & Data:This study generalizes the prime radical of $\sqrt{I}$ where it denotes by $\sqrt[n+1]{I}$, for $n\in \mathbb{Z}^{+}$.
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Conclusion & Impact:Furthermore, two open problems are presented.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:prime ring · prime ideal · prime radical
Abstract
Let $R$ be a ring, $I$ be an ideal of $R$, and $\sqrt{I}$ be a prime radical of $I$. This study generalizes the prime radical of $\sqrt{I}$ where it denotes by $\sqrt[n+1]{I}$, for $n\in \mathbb{Z}^{+}$. This generalization is called $n$-prime radical of ideal $I$. Moreover, this paper shows that $R$ is isomorphic to a subdirect sum of ring $H_{i}$ where $% H_{i}$ are $n$-prime rings. Furthermore, two open problems are presented.
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Cite This Article
Camcı, D. K., Yeşil, D., Mekera, R., Camcı, Ç. (2023). A Generalization of the Prime Radical of Rings. Natural and Applied Sciences Journal, Cilt: 6 Sayı: 2, 61–69. https://doi.org/10.38061/idunas.1401075