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

 

All $ n$-cotilting modules are pure-injective


Author: Jan Stovícek
Journal: Proc. Amer. Math. Soc. 134 (2006), 1891-1897
MSC (2000): Primary 16D90; Secondary 16E30, 03E75
Published electronically: January 17, 2006
MathSciNet review: 2215116
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Abstract: We prove that all $ n$-cotilting $ R$-modules are pure-injective for any ring $ R$ and any $ n \ge 0$. To achieve this, we prove that $ {^{\perp_1} U}$ is a covering class whenever $ U$ is an $ R$-module such that $ {^{\perp_1} U}$ is closed under products and pure submodules.


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Additional Information

Jan Stovícek
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Address at time of publication: Institutt for Matematiske FAG, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Email: stovicek@karlin.mff.cuni.cz, stovicek@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08256-6
PII: S 0002-9939(06)08256-6
Received by editor(s): February 22, 2005
Published electronically: January 17, 2006
Additional Notes: This research was supported by a grant of the Industrie Club Duesseldorf and by GAČR 201/05/H005.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.