Abstract
Let R be a ring and let t be a torsion preradical, R is said to have the splitting property, provided that for every left R-module M, the torsion submodule t ( M ) of M is a direct summand of M. The characterization of rings with this property is a classical problem (in particular the Goldie and Dickson torsion theories have been studied) that for noncommutative rings remains open. We consider the problem for the algebra C * , associated to a coalgebra C, and the torsion preradical Rat. It is shown that if C * has the splitting property with respect a Rat, then C is finite dimensional.
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