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APPLICATIONS OF COTORSION PAIRS

Published online by Cambridge University Press:  17 November 2003

HENNING KRAUSE  and
ØYVIND SOLBERG
HENNING KRAUSE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, [email protected] Present address: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT [email protected]
ØYVIND SOLBERG
Affiliation:
Institutt for Matematiske Fag, NTNU, N-7491 Trondheim, [email protected]
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Abstract

For an artin algebra $\Lambda$, cotorsion pairs are studied for the category ${\rm mod}\Lambda$ of finitely presented $\Lambda$-modules and for the category ${\rm Mod}\Lambda$ of all $\Lambda$-modules. It is shown that every cotorsion pair for ${\rm mod}\Lambda$ induces a cotorsion pair for ${\rm Mod}\Lambda$. This has some interesting applications, even for the category of finitely presented modules. Another theme of the paper is the interplay between cotorsion and torsion pairs. This leads to a conjecture which is an analogue of the telescope conjecture in stable homotopy theory.

Keywords

16E30 (primary)16D90 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 631 - 650
Copyright
The London Mathematical Society 2003

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