Bounded submodules of modules

Let m, n be positive integers such that mless-than-or-equals, slantn and k be a field. We consider all pairs (B,A) where B is a finite dimensional Tn-bounded k[T]-module and A is a submodule of B which is Tm-bounded. They form the objects of the submodule category image which is a Krull–Schmidt category with Auslander–Reiten sequences. The case m=n deals with submodules of k[T]/Tn-modules and has been studied well. In this paper we determine the representation type of the categories image also for the cases where m