Geodesic
Unequivocal Rings
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 679-690

Voir la notice de l'article provenant de la source Cambridge University Press

For any radical property Q, a nonzero simple ring (all rings in this paper are assumed to be associative) must make up its mind so to speak and must be either Q radical or Q semi-simple. Every Q thus divides the class of all nonzero simple rings into two disjoint classes. Conversely any partition of the nonzero simple rings into two disjoint classes leads to at least two radicals [1, p. 16]. 
Divinsky, N. Unequivocal Rings. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 679-690. doi: 10.4153/CJM-1975-076-5
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