GENERALIZATIONS OF INJECTIVE MODULES

Abstract

Let R be a ring with identity. Given a positive integer n, a unitary right R-module X is called n–injective provided, for every n-generated right ideal A of R, every R-homomorphism φ : A → X can be lifted to R. In this note we investigate this and related injectivity conditions and show that there are many rings R which have an n–injective module which is not (n+1)– injective.