The Good Journal

We study the classes of modules which are generated by a silting module. In the case of either hereditary or perfect rings, it is proved that these are exactly the torsion T such that the regular module has a special T-preenvelope. In particular, every torsion-enveloping class in Mod-R are of the form Gen(T) for a minimal silting module T. For the dual case, we obtain for general rings that the covering torsion-free classes of modules are exactly the classes of the form Cogen(T), where T is a cosilting module.