Flat Mittag-Leffler modules over countable rings

Bazzoni, Silvana; Šťovíček, Jan

doi:10.1090/S0002-9939-2011-11070-0

Flat Mittag-Leffler modules over countable rings
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by Silvana Bazzoni and Jan Šťovíček PDF

Proc. Amer. Math. Soc. 140 (2012), 1527-1533 Request permission

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 Šaroch and Trlifaj, that the class of flat Mittag-Leffler modules is not precovering in $\operatorname {Mod}\text {-}{R}$ unless $R$ is right perfect.

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