Injective Modules Relative To a Preradical

Abstract

The concept ofߩ-injective modules (where ߩ is a preradical) is introduced in this work as ageneralization of injective modules. The definition of ߩ-injectivity unifies several definitions ongeneralizations of injectivity such as nearly injective modules and special injective modules. Manycharacterizations and properties of ߩ-injectivity are given. We study the endomorphisms rings ofߩ-injective modules. The results of this work unify and extend many results in the literature.