IMCS/Publications/BASM/Issues/BASM n.2 (36), 2001/

On some bijections between ideals, classes of modules and preradicals of R-mod.

Authors: Caşu Alexei


The three-sided relations are studied between the ideals of ring R, classes of R-modules and preradicals of the category R-Mod. Every ideal is accompanied by two preradicals (r(I), r(I)) and three classes of modules (τI, A(I), FI). Modifying the condition on I, the reactions of associated objects are investigated. A series of bijections is obtained between ideals with suitable properties, classes of modules closed under some constructions and preradicals of special types. This general scheme joins together some known results, which are supplemented by conditions on classes, filters etc.