Flat Mittag-Leffler modules over countable rings

Details Flat Mittag-Leffler modules over countable rings Flat Mittag-Leffler modules over countable rings

2010-07-28

arxiv.org/abs/1007.4977v2

Mathematics

Rings and Algebras

7 pages; version 2: minor changes, more explanation added in the proof of Theorem 6 and Lemma 7, references added and updated

Scientific paper

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.

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