Abstract
A coalgebraC is said to have the splitting property if the maximal rational submoduleRat(M) of any leftC*-moduleM is a direct, summand of it. In this paper we prove that a coalgebraC satisfying this property is finite dimensional. Cocommutative coalgebras such thatRat(M) is a direct summand for any finitely generated leftC*-moduleM are explicitly described.
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