Abstract
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].
Publisher
Canadian Mathematical Society
Cited by
19 articles.
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1. Radical Classes Closed Under Products;Analele Universitatii "Ovidius" Constanta - Seria Matematica;2013-11-01
2. Compact elements in the lattice of radicals;Acta Mathematica Hungarica;2005-05
3. RADICALS THAT DO NOT CONTAIN NON-ZERO *-RINGS;Quaestiones Mathematicae;1999-09
4. Additive groups of unequivocal rings;Acta Mathematica Hungarica;1998
5. Radicals of a ring;Communications in Algebra;1994-01