Direct sum decompositions of indecomposable injective modules
Bull. Korean Math. Soc. 1998 Vol. 35, No. 1, 33-43
Sang Cheol Lee Chonbuk National University
Abstract : 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.