ℒ-Injective Hulls of Modules

Abstract

Let R be a ring and ℒ a class of R-modules. An R-module N is called ℒ-injective if for all L ∈ ℒ. An ℒ-injective hull of an R-module M is defined to be a homomorphism φ: M → F with F ℒ-injective such that for any monomorphism f: M → F′ with F′ ℒ-injective, there is a monomorphism g: F → F′ satisfying gφ = f. The aim of this paper is to study ℒ-injective hulls and their relations with ℒ-injective envelopes in Enochs' sense.