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Abstract
Snider showed that the class of radicals of rings has a natural lattice structure. The same is true for any universal class of near-rings. We show that the classes of hereditary and ideal-hereditary radicals, inter alia, are complete sublattices. Atoms of certain sublattices are discussed. If N is a universal class of near-rings containing the universal class R of rings, we show that there exists an injection of the lattice of radicals L R in R into the lattice L N of radicals in N, whose restriction to the hereditary radicals is a lattice monomorphism. There is also a lattice epimorphism from L N onto L R . Finally, some results are obtained concerning special radicals.