Bulletin of the
Korean Mathematical Society BKMS

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 injectives? It will be proved that the Matlis problem has an affirmative answer when $M$ is a multiplication module, and that a weaker condition than that of $M$ being a multiplication module can be given to the module $M$ when $M$ is a countable direct sum of indecomposable injectives.

Keywords: indecomposable injective module, multiplication module, weak multiplication module

MSC numbers: Primary 16D50, 16D70, 13E05, 13E10