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 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. Keywords : indecomposable injective module, multiplication module, weak multiplication module MSC numbers : Primary 16D50, 16D70, 13E05, 13E10 Downloads: Full-text PDF