Publication at Faculty of Mathematics and Physics |
2010
Abstract
We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras R: the Baer, and the Mittag-Leffler ones. A right module M is called Baer if Ext(M,T) = 0 for all torsion modules T, and M is Mittag-Leffler in case the canonical map from (M otimes prod Q_i) to prod (M otimes Q_i) is injective for an each sequence of left modules (Q_i).
We show that a module M is Baer iff it is p-filtered where p is the preprojective component of R. We apply this to prove that the universal localization of a Baer module with respect to a complete tube in the AR-quiver of R is always projective.
In the final section, we give a complete classification of the Mittag-Leffler modules