On the structure of indecomposable injective modules¹

Abstract

For a ring R, the following two conditions are equivalent:. (1) If E is an indecomposable injective right R-module, then End ER is a field (not necesarily commutative). (2) Every co-irreducible rigtht ideal is critical. Since (2) has been characterized ideal-theoretically, this amounts to an ideal-theoretical characterization of (1). These rings come up to the study of (QI) rings in which every quasi-injective module is injective.