On the cogeneration of cotorsion pairs

Paul C. Eklof; Saharon Shelah; Jan Trlifaj

doi:10.1016/j.jalgebra.2003.09.018

On the cogeneration of cotorsion pairs

Paul C. Eklof^*, Saharon Shelah, Jan Trlifaj

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let R be a Dedekind domain. Recently, 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.

Original language	English
Pages (from-to)	572-578
Number of pages	7
Journal	Journal of Algebra
Volume	277
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2003.09.018
State	Published - 15 Jul 2004

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abstract = "Let R be a Dedekind domain. Recently, 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.",

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N2 - Let R be a Dedekind domain. Recently, 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.

AB - Let R be a Dedekind domain. Recently, 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.

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On the cogeneration of cotorsion pairs

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