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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):121-132; doi:10.1112/blms/bdl019
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© 2006 London Mathematical Society

All tilting modules are of countable type

Jan Stovícek

Institutt for Matematiske Fag
NTNU
N-7491 Trondheim
Norway
stovicek{at}math.ntnu.no

Jan Trlifaj

Charles University
Faculty of Mathematics and Physics
Department of Algebra
Sokolovská 83
186 75 Prague 8
Czech Republic
trlifaj{at}karlin.mff.cuni.cz

Received 30 March 2005. Revision received 2 December 2005.

Let R be a ring and T an (infinitely generated) tilting module. Then T is of countable type; that is, there is a set, C, of modules possessing a projective resolution consisting of countably generated projective modules such that the tilting class T{perp} equals C{perp}. Moreover, a cotorsion pair C = (A, B) is tilting if and only if: C is hereditary, all modules in A have finite projective dimension, and B is closed under arbitrary direct sums.


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