Injective Modules Relative To a Preradical

Abstract

The concept of ðœŒ-injective modules (where 𜌠is a preradical) is introduced in this work as a generalization of injective modules. The definition of ðœŒ-injectivity unifies several definitions on generalizations of injectivity such as nearly injective modules and special injective modules. Many characterizations and properties of ðœŒ-injectivity are given. We study the endomorphisms rings of ðœŒ-injective modules. The results of this work unify and extend many results in the literature.