Pretorsions in modules and associated closure operators

This article contains the results on the pretorsions of the module category $R$-Mod and on the closure operators defined by them. The pretorsions of $R$-Mod can be described in diverse forms: by classes of modules, filters of left ideals of $R$, closure operators, dense submodules, etc. In the set $\mathbb{PT}$ of pretorsions of $R$-Mod the main operations are studied, as well as their expressions in terms of classes of modules, filters, operators, etc. The approximations of pretorsions by jansian pretorsions and by torsions are mentioned.