Bounded submodules of modules

[摘要] Let m, n be positive integers such that m <= n and k be a field. We consider all pairs (B, A) where B is a finite dimensional T-n -bounded k[T]-module and A is a submodule of B which is T-m-bounded. They form the objects of the submodule category Y-m(k[T]/T-n) which is a Krull-Schmidt category with Auslander-Reiten sequences. The case m = n deals with submodules of k[T]/T-n-modules and has been studied well. In this paper we determine the representation type of the categories Y-m(k[T]/T-n) also for the cases where m < n: It turns out that there are only finitely many indecomposables in Y-m(k[T]/T-n) if either m < 3, n < 6, or (m, n) = (3, 6); the category is tame if (m, n) is one of the pairs (3, 7), (4, 6), (5, 6), or (6, 6); otherwise, Y-m (k [T]/T-n) has wild representation type. Moreover, in each of the finite or tame cases we describe the indecomposables and picture the Auslander-Reiten quiver. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2005-12-01