BASIC PRERADICALS AND MAIN INJECTIVE MODULES

Abstract

We consider those injective modules that determine every left exact preradical and we call them main injective modules. We construct a main injective module for every ring and we prove some of its properties. In particular we give a characterization, in terms of main injective modules, of rings with a dimension defined by a filtration in the lattice of left exact preradicals. We define also the concept of basic preradical and prove some of its properties. In particular we prove that the class of all basic preradicals is a set, giving a bijective correspondence with the set of all left exact preradicals.