Flat Mittag-Leffler modules over countable rings
Rings and Algebras
2012-07-10 v2 Algebraic Geometry
Abstract
We show that over any ring, the double Ext-orthogonal class to all flat Mittag-Leffler modules contains all countable direct limits of flat Mittag-Leffler modules. If the ring is countable, then the double orthogonal class consists precisely of all flat modules and we deduce, using a recent result of \v{S}aroch and Trlifaj, that the class of flat Mittag-Leffler modules is not precovering in Mod-R unless R is right perfect.
Keywords
Cite
@article{arxiv.1007.4977,
title = {Flat Mittag-Leffler modules over countable rings},
author = {Silvana Bazzoni and Jan Stovicek},
journal= {arXiv preprint arXiv:1007.4977},
year = {2012}
}
Comments
7 pages; version 2: minor changes, more explanation added in the proof of Theorem 6 and Lemma 7, references added and updated