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Bulletin of the London Mathematical Society (1)

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AUSLANDER–REITEN TRIANGLES AND A THEOREM OF ZIMMERMANN
HENNING KRAUSE
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 3 / June 2005

Published online by Cambridge University Press:

01 June 2005, pp. 361-372

Print publication:

June 2005
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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.