Galois connections between lattices of preradicals induced by ring epimorphisms

We continue the study of Galois connections between the lattices of preradicals of two rings [Formula: see text] and [Formula: see text] induced by an adjoint pair of functors between the categories [Formula: see text]-Mod and [Formula: see text]-Mod. In this paper, we focus on the functor triple induced by any ring homomorphism [Formula: see text], and particularly when it is a ring epimorphism. We give additional results when the epimorphism is flat and when it is projective.