# Sh:814

- Eklof, P. C., Shelah, S., & Trlifaj, J. (2004).
*On the cogeneration of cotorsion pairs*. J. Algebra,**277**(2), 572–578. arXiv: math/0405117 DOI: 10.1016/j.jalgebra.2003.09.018 MR: 2067620 -
Abstract:

Let R be a Dedekind domain. Enochs’ solution of the Flat Cover Conjecture was extended as follows: (*) If \mathfrak C is a cotorsion pair generated by a class of cotorsion modules, then \mathfrak 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 \mathfrak C is not cogenerated by a set whenever \mathfrak C is a cotorsion pair generated by a set which contains a non-cotorsion module. - published version (7p)

Bib entry

@article{Sh:814, author = {Eklof, Paul C. and Shelah, Saharon and Trlifaj, Jan}, title = {{On the cogeneration of cotorsion pairs}}, journal = {J. Algebra}, fjournal = {Journal of Algebra}, volume = {277}, number = {2}, year = {2004}, pages = {572--578}, issn = {0021-8693}, doi = {10.1016/j.jalgebra.2003.09.018}, mrclass = {16S90}, mrnumber = {2067620}, mrreviewer = {Rafail Alizade}, doi = {10.1016/j.jalgebra.2003.09.018}, note = {\href{https://arxiv.org/abs/math/0405117}{arXiv: math/0405117}}, arxiv_number = {math/0405117} }