On subinjectivity domains of finitely generated modules

A module M is called FG-injective if every homomorphism from M to a finitely generated module K factors through an injective module, generalizing the injective modules properly. If the subinjectivity domain of M consists of exactly the FG-injective modules, then M is said to be fg-indigent. Properties of FG-injective modules and of fg-indigent modules are studied, and the concept of si-portfolio is considered for finitely generated modules. The collection of all subinjectivity domains of all finitely generated modules is also considered, and the cases where this collection forms a chain or has a single or two elements are investigated.