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

 

Abstract elementary classes induced by tilting and cotilting modules have finite character


Author: Jan Trlifaj
Journal: Proc. Amer. Math. Soc. 137 (2009), 1127-1133
MSC (2000): Primary 03C95, 16E30; Secondary 03C60, 16D90
Published electronically: October 1, 2008
MathSciNet review: 2457454
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Abstract: Let $ R$ be a ring and $ \mathcal C$ be a cotilting class of $ R$-modules. Define $ A \leq B$ by $ A \subseteq B$ and $ A, B, B/A \in \mathcal C$. Then $ (\mathcal C, \leq)$ is an abstract elementary class of finite character. An analogous result holds for all abstract elementary classes induced by tilting modules.


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Additional Information

Jan Trlifaj
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: trlifaj@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09618-4
PII: S 0002-9939(08)09618-4
Keywords: Abstract elementary class of finite character, definable class, tilting module, cotilting module, Ext
Received by editor(s): December 14, 2007
Received by editor(s) in revised form: April 15, 2008
Published electronically: October 1, 2008
Additional Notes: This research was supported by GAČR 201/06/0510 and MSM 0021620839
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.