Torsion theories, radicals and closure operators in the category of rings

In 1971, Joachim Lambek published a result which gives an equivalence between torsion theories (B, C) and idempotent radicals T in the category Mod R, establishing some properties of the classes of R-modules B and C and performing a characterization of these classes using the radical T. Recently, D. Dikranjan, W. Tholen and G. Castellini have defined, in this category, new closure operators based on pre-radicals and reciprocally, they have defined radicals based on closure operators.;In this thesis we have made some modifications to these results, defining new concepts and finding some conditions to be satisfied by the classes B and C in order to establish some connection between torsion theories and radicals in the category Rng. We have also defined closure operators using pre-radicals and vice versa, establishing a non bijective correspondence between these two concepts in this category.