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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical.
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Key Findings & Data:In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical.
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Conclusion & Impact:We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Jacobson radical · quasinilpotent elements · elements with singleton spectra
Abstract
In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical. We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.
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Cite This Article
CAO, P., WANG, X. (2019). When do quasinilpotents lie in the Jacobson radical?. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 132–142. https://ajindex.com/articles/212750