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Abstract
In [Citation8] L. Salce introduced the notion of a cotorsion pair (β±, π) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proven to be useful in a variety of settings. A significant result of cotorsion theory proven by Eklof and Trlifaj is that if a pair (β±, π) of classes of R-modules is cogenerated by a set, then it is complete [Citation1]. Recently Fu, Herzog, Guil, and Torrecillas developed the ideal approximation theory [Citation6], [Citation4]. In this article we look at a result motivated by the Eklof and Trlifaj argument for an ideal β when it is generated by a set of homomorphisms.
ACKNOWLEDGMENT
The author is very thankful to Edgar Enochs for his contributions and suggestions during the course of preparing this manuscript and would also like to thank the referee for the useful comments and corrections.
Notes
Communicated by S. Bazzoni.