Proceedings of the American Mathematical Society

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

Author(s): Jan Trlifaj
Journal: Proc. Amer. Math. Soc. 137 (2009), 1127-1133.
MSC (2000): Primary 03C95, 16E30; Secondary 03C60, 16D90
Posted: October 1, 2008
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Abstract: Let

be a ring and $\mathcal C$ be a cotilting class of

-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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03C95, 16E30, 03C60, 16D90

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: 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
Posted: October 1, 2008
Additional Notes: This research was supported by GACR 201/06/0510 and MSM 0021620839
Communicated by: Julia Knight
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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