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Lower bounds for faithful,preinjective modules

Authors:	Luise Unger

Institution:	(1) Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße, 4800 Bielefeld, FRG

Abstract:	Let $k\overrightarrow \Delta$ be the path algebra for some representation-infinite quiver $\overrightarrow \Delta$ over some field k. There exists a bound $m(\overrightarrow \Delta )$ such that ^mI is faithful for all indecomposable injective $k\overrightarrow \Delta$ -modules I and all $m \geqslant m(\overrightarrow {\Delta )}$ , and such that there exists an indecomposable injective $k\overrightarrow \Delta$ -module J satisfying that ${}_\tau m(\overrightarrow {\Delta )} - I_J$ J is not faithful, denotes the Auslander-Reiten-translation. Let m() be the maximum of the $m(\overrightarrow {\Delta )}$ taken over all possible orientations of the underlying graph . In this article we determine the bounds m() for representation-infinite quivers $\overrightarrow \Delta$ for which is a tree.

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