Flat Mittag-Leffler modules over countable rings
arXiv:1007.4977 · doi:10.1090/S0002-9939-2011-11070-0
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 Å aroch and Trlifaj, that the class of flat Mittag-Leffler modules is not precovering in Mod-R unless R is right perfect.
7 pages; version 2: minor changes, more explanation added in the proof of Theorem 6 and Lemma 7, references added and updated