A survey of results on radicals and torsions in modules

Abstract

In this work basic results of the author on radicals in module categories are presented in a short form. Principal topics are: types of preradicals and their characterizations; classes of \(R\)-modules and sets of left ideals of \( R\); notions and constructions associated to radicals; rings of quotients and localizations; preradicals in adjoint situation; torsions in Morita contexts; duality between localizations and colocalizations; principal functors and preradicals; special classes of modules; preradicals and operations in the lattices of submodules; closure operators and preradicals.