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

On $J$-rigid rings

Soraya KARİMİ
Shervin SAHEBİ
Mohammad HABİBİ
Pages
1815–1823
Publication Date
2019-12-08
DOI
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AI Summary & Key Takeaways

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

Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $R$ be a ring with an endomorphism $\sigma$.
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Key Findings & Data:We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties.
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Conclusion & Impact:Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Rigid rings · Reduced rings · Jacobson radical

Abstract

Let $R$ be a ring with an endomorphism $\sigma$. We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties. It is proved that a ring $R$ is $\sigma$-$J$-rigid if and only if $R[[x;\sigma]]$ is $\bar\sigma$-$J$-rigid, while the $\sigma$-$J$-rigid property is not Morita invariant. Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

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Cite This Article

KARİMİ, S., SAHEBİ, S., HABİBİ, M. (2019). On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1815–1823. https://ajindex.com/articles/669334

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