%0 Journal Article
%T Lattice structure of torsion classes for hereditary artin algebras
%A Claus Michael Ringel
%J Mathematics
%D 2014
%I arXiv
%X Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules. For the case of A being the path algebra of a quiver, this result has recently been established by Iyama-Reiten-Thomas-Todorov and our proof follows closely their considerations.
%U http://arxiv.org/abs/1402.1260v1