  Let $A$ be a pseudocompact (or profinite) algebra, so $A=C^*$ where $C$ is a
coalgebra. We show that the if the semiartinian part (the "Dickson" part) of
every $A$-module $M$ splits off in $M$, then $A$ is semiartinian, also giving a
positive answer in the case of algebras arising as dual of coalgebras
(pseudocompact algebras), to a well known conjecture of Faith.
