{"paper":{"title":"Systems of submodules and a remark by M.C.R. Butler","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Markus Schmidmeier","submitted_at":"2005-07-27T12:47:50Z","abstract_excerpt":"Fix a poset $P$ and a natural number $n$. For various commutative local rings $\\Lambda$, each of Loewy length $n$, consider the category $\\textrm{sub}_\\Lambda P$ of $\\Lambda$-linear submodule representations of $P$. We give a criterion for when the underlying translation quiver of a connected component of the Auslander-Reiten quiver of $\\textrm{sub}_\\Lambda P$ is independent of the choice of the base ring $\\Lambda$. If $\\mathcal P$ is the one-point poset and $\\Lambda=\\mathbb Z/p^n$ for $p$ a prime number, then $\\textrm{sub}_\\Lambda P$ consists of all pairs $(B;A)$ where $B$ is a finite abelian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507559","kind":"arxiv","version":2},"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"}