ar X iv : 0 80 4 . 08 15 v 1 [ m at h . R T ] 4 A pr 2 00 8 LARGE TILTING MODULES AND REPRESENTATION TYPE LIDIA
نویسنده
چکیده
We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (infinite dimensional) tilting module W that generates the divisible modules. Finally, we extend to the wild case some results on Baer modules and torsion-free modules proven in [5] for tame hereditary algebras.
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