  L. Salce introduced the notion of a cotorsion pair (F,C) in the category of
abelian groups. But his definitions and basic results carry over to more
general abelian categories and have proven useful in a variety of settings. A
significant result of cotorsion theory proven by Eklof and Trlifaj is that if a
pair (F,C) of classes of R-modules is cogenerated by a set, then it is
complete. Recently Herzog, Fu, Asensio and Torrecillas developed the ideal
approximation theory. In this article we look at a result motivated by the
Eklof-Trlifaj argument for an ideal I when it is generated by a set of
homomorphisms.
