Coronel-Suárez, Angy C.

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Torsion theories, radicals and closure operators in the category of rings
(2009-05) Coronel-Suárez, Angy C.; Castellini, Gabriele; College of Arts and Sciences - Sciences; Cáceres, Luis F.; Walker, Uroyoán; Department of Mathematics; Palomera, Rogelio
In 1971, Joachim Lambek published a result which gives an equivalence between torsion theo- ries (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 conection 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 correspon- dence between these two concepts in this category.