Proceedings of the American Mathematical Society

Author(s): Jan Stovícek
Journal: Proc. Amer. Math. Soc. 134 (2006), 1891-1897.
MSC (2000): Primary 16D90; Secondary 16E30, 03E75
Posted: January 17, 2006
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Abstract: We prove that all

-cotilting

-modules are pure-injective for any ring

and any $n \ge 0$ . To achieve this, we prove that ${^{\perp_1} U}$ is a covering class whenever

is an

-module such that ${^{\perp_1} U}$ is closed under products and pure submodules.

1.: L. Angeleri Hügel and F. Coelho, Infinitely generated tilting modules of finite projective dimension, Forum Math. 13 (2001), 239-250. MR 1813669 (2002b:16009)
2.: L. Angeleri Hügel, D. Herbera and J.Trlifaj, Tilting modules and Gorenstein rings, to appear in Forum. Math.
3.: S. Bazzoni, A characterisation of -cotilting and -tilting modules, J. Algebra 273 (2004), 359-372. MR 2032465
4.: S. Bazzoni, Cotilting modules are pure-injective, Proc. Amer. Math. Soc. 131 (2003), 3665-3672. MR 1998172 (2004f:16049)
5.: S. Bazzoni, -cotilting modules and pure-injectivity, Bull. London Math. Soc. 36 (2004), 599-612. MR 2070436 (2005d:16012)
6.: S. Bazzoni, Tilting and cotilting modules over Prüfer domains, preprint.
7.: S. Bazzoni, R. Göbel and L. Strüngmann, Pure injectivity of -cotilting modules: the Prüfer and the countable case, to appear in Archiv der Mathematik.
8.: P. C. Eklof and A. H. Mekler, Almost Free Modules, North-Holland Math. Library, Elsevier, Amsterdam, 1990. MR 1055083 (92e:20001)
9.: P. C. Eklof and J. Trlifaj, Covers induced by Ext, J. Algebra 231 (2000), 640-651. MR 1778163 (2001f:16021)
10.: R. Göbel and J. Trlifaj, Cotilting and a hierarchy of almost cotorsion groups, J. Algebra 224 (2000), 110-122. MR 1736696 (2001a:20100)
11.: P. Griffith, On a subfunctor of Ext, Arch. Math. XXI (1970), 17-22. MR 0262356 (41:6964)
12.: M. Prest, Model theory and modules, London Math. Soc. Lect. Note Ser. 130, Cambridge University Press, 1988. MR 0933092 (89h:03061)
13.: L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), Academic Press, 11-32. MR 0565595 (81j:20078)
14.: J. Šaroch and J. Trlifaj, Completeness of cotorsion pairs, preprint.
15.: J. Trlifaj, Infinite dimensional tilting modules and cotorsion pairs, to appear in the Handbook of Tilting Theory (London Math. Soc. Lect. Notes).
16.: J. Xu, Flat Covers of Modules, Lecture Notes in Math. 1634, Springer-Verlag, New York, 1996. MR 1438789 (98b:16003)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16D90, 16E30, 03E75

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

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