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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Flat Mittag-Leffler modules over countable rings


Authors: Silvana Bazzoni and Jan Šťovíček
Journal: Proc. Amer. Math. Soc. 140 (2012), 1527-1533
MSC (2010): Primary 16D40; Secondary 16E30, 03E75
Published electronically: September 6, 2011
MathSciNet review: 2869137
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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}$-$ {R}$ unless $ R$ is right perfect.


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Additional Information

Silvana Bazzoni
Affiliation: Dipartimento di Matematica Pura e Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy
Email: bazzoni@math.unipd.it

Jan Šťovíček
Affiliation: Department of Algebra, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovska 83, 186 75 Praha 8, Czech Republic
Email: stovicek@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11070-0
PII: S 0002-9939(2011)11070-0
Keywords: Flat Mittag-Leffler modules, precovers, Ext-orthogonal classes
Received by editor(s): July 28, 2010
Received by editor(s) in revised form: January 18, 2011
Published electronically: September 6, 2011
Additional Notes: The first author was supported by MIUR, PRIN 2007, project “Rings, algebras, modules and categories” and by Università di Padova (Progetto di Ateneo CPDA071244/07 “Algebras and cluster categories”).
The second author was supported by the Eduard Čech Center for Algebra and Geometry (LC505).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.