Bounded submodules of modules

Abstract: Let , be positive integers such that and be a field. We consider all pairs where is a finite dimensional -bounded -module and is a submodule of which is -bounded. They form the objects of the submodule category which is a Krull–Schmidt category with Auslander–Reiten sequences. The case deals with submodules of -modules and has been studied well. In this paper we determine the representation type of the categories also for the cases where : It turns out that there are only finitely many indecomposables in if either , , or ; the category is tame if is one of the pairs , , , or ; otherwise, has wild representation type. Moreover, in each of the finite or tame cases we describe the indecomposables and picture the Auslander–Reiten quiver. [Copyright &y& Elsevier]