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When Do Quasinilpotents Lie In The Jacobson Radical?

Peng Cao,Xin Wang

TURKISH JOURNAL OF MATHEMATICS（2019）

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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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Key words
Jacobson radical,quasinilpotent elements,elements with singleton spectra
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