∑-injective modules over left duo and left distributive rings Original Research Article

We show that over any left distributive or left duo ring R there exists a 1-1 correspondence between ∑-injective indecomposable left modules and completely prime ideals P such that the left classical localization R(P) exists and is a left noetherian ring. Notice that the well-known theorems of Krause and Matlis can be reformulated in terms of such a correspondence.