Generalized monoform and quasi injective modules

Abstract

For a torsion radical F (arising from an idempotent filter of right ideals) and a unital right R-module M over a ring R, let DM be the F-divisible hull DM/M = F (EM/M), where EM is the injective hull of M. Let 0 ^ : N^> M be any nonzero homomorphism whatever from any F-dense submodule NCM Then M is F-quasi-injective if each such extends to a homomorphism of M-^M;