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

On $J$-rigid rings

Soraya Karimi(Islamic Azad University)0000-0002-5690-4602
Shervin Sahebi(Islamic Azad University)0000-0003-0114-8798
Mohammad Habibi(Tafresh University)0000-0003-1317-1434
Pages
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Publication Date
2019-12-08
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⚡ 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

Karimi, S., Sahebi, S., Habibi, M. (2019). On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 6. https://doi.org/10.15672/HJMS.2018.646

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