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AUSLANDER–REITEN TRIANGLES AND A THEOREM OF ZIMMERMANN

Published online by Cambridge University Press:  01 June 2005

HENNING KRAUSE
HENNING KRAUSE
Affiliation:
Institut für Mathematik, Universität Paderborn, 33095 Paderborn, [email protected]
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Abstract

A classical theorem of Zimmermann describes the relation between almost split sequences in the category of finitely presented modules and those in the category of all modules over some fixed ring. An analogue of Auslander–Reiten triangles in triangulated categories is proved in this paper. This is used to explain the relation between different existence results for Auslander–Reiten triangles, which are based either on Brown's representability theorem, or on the existence of Serre functors.

Keywords

18E3016G70 (primary)14F0555U35 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 3 , June 2005 , pp. 361 - 372
Copyright
© The London Mathematical Society 2005

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