Matlis posed the following question in 1958: if N is a direct summand of a direct sum M of indecomposable injectives, then is N itself a direct sum of indecomposable innjectivesulcorner It will be proved that the Matlis problem has an affirmative answer when M is a multiplication module, and that a weaker condition then that of M being a multiplication module can be given to module M when M is a countable direct sum of indecomposable injectives.