ABSTRACT
The material in this chapter comes from [40] where the filter of divisibility
D(G) = {right ideals I ⊂ End(G) IG = G}
is studied. This filter is nicely structured. We are most interested in the subfilters of D(M) called Gabriel filters that correspond to a hereditary torsion class of right E-modules K such that K⊗EG = 0. In particular, we will show that D(G) is in many interesting cases bounded by an idempotent ideal ∆. That is, there is an ideal ∆ of End(G) such that ∆2 = ∆ and such that IG = G implies ∆ ⊂ I.
