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.
CAO, PENG and WANG, XIN
"When do quasinilpotents lie in the Jacobson radical?,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/11