Abstract
We define a partition of the lattice R-pr of preradicals over pure semisimple hereditary rings, and describe the equivalence classes of the idempotent radicals, which correspond to splitting torsion theories induced by the Ext-injective partition of R-ind. Specifically, in a particular class of these rings, which have only two non-isomorphic simple modules, by means of the strong preinjective partition of R-ind, we enumerate all idempotent preradicals, all radicals and all torsion theories, and we also give a description of the structure of all preradicals.
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