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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

When do quasinilpotents lie in the Jacobson radical?

Peng CAO
Xin WANG
Pages
132–142
Publication Date
2022-11-04
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show thatsome conditions with -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 withsingleton 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 thatsome conditions with -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 withsingleton spectra.
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Key Findings & Data:In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show thatsome conditions with -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 withsingleton spectra.
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Conclusion & Impact:In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show thatsome conditions with -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 withsingleton spectra.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show thatsome conditions with -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 withsingleton spectra.

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Cite This Article

CAO, P., WANG, X. (2022). When do quasinilpotents lie in the Jacobson radical?. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 132–142. https://ajindex.com/articles/607720

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References (7)

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