The splitting problem for coalgebras: a direct approach
  In this note we give a different and direct short proof to a previous result of Nastasescu and Torrecillas in \cite{NT} stating that if the rational part of any right $C^*$ module $M$ is a direct sumand in $M$ then $C$ must be finite dimensional (the splitting problem for coalgebras). 
M. C. Iovanov
math.RA math.RT