Publication at Faculty of Mathematics and Physics |
2010
Abstract
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 tilting module L that generates all modules without preprojective direct summands.
We show that the behavior of L over its endomorphism ring determines the representation type of R. A similar result holds true for the tilting module W that generates all divisible modules.
Finally, we extend to the wild case the results on Baer modules and torsion-free modules proven earlier for tame hereditary algebras.