On the cogeneration of cotorsion pairs
Logic
2007-05-23 v1
Abstract
Let R be a Dedekind domain. Enochs' solution of the Flat Cover Conjecture was extended as follows: (*) If C is a cotorsion pair generated by a class of cotorsion modules, then C is cogenerated by a set. We show that (*) is the best result provable in ZFC in case R has a countable spectrum: the Uniformization Principle UP^+ implies that C is not cogenerated by a set whenever C is a cotorsion pair generated by a set which contains a non-cotorsion module.
Keywords
Cite
@article{arxiv.math/0405117,
title = {On the cogeneration of cotorsion pairs},
author = {Paul C. Eklof and Saharon Shelah and Jan Trlifaj},
journal= {arXiv preprint arXiv:math/0405117},
year = {2007}
}