{"paper":{"title":"Bounded Submodules of Modules","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Markus Schmidmeier","submitted_at":"2004-08-13T18:33:14Z","abstract_excerpt":"Let $m$, $n$ be positive integers such that $m\\leq n$. 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 $S_m(k[T]/T^n)$ 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 manuscript we determine the representation type of the categories $S_m(k[T]/T^n)$ also for the cases where $m<n$: It turns out that there are only finitely many indecomposabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408181","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}