SURVEY ARTICLE

A survey of results on radicals and torsions in modules

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD – 2028 MOLDOVA

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.

Keywords: ring, module, lattice, (pre)radical, torsion, localization, adjoint functor, Morita context, closure operator.

MSC: 16D90, 16S90

Received: 18.12.2015

Language: English

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