Every module is an inverse limit of injectives

Abstract

It is shown that any left module A A over a ring R R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives. If R R is left Noetherian, A A can also be written as the inverse limit of a system of surjective homomorphisms of injectives. Some questions are raised.