All $n$-cotilting modules are pure-injective
Author:
Jan Šťovíček
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1891-1897
MSC (2000):
Primary 16D90; Secondary 16E30, 03E75
DOI:
https://doi.org/10.1090/S0002-9939-06-08256-6
Published electronically:
January 17, 2006
MathSciNet review:
2215116
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Abstract | References | Similar Articles | Additional Information
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 Šťovíček
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
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.