{"paper":{"title":"Minimal relations and catenary degrees in Krull monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alfred Geroldinger, Yushuang Fan","submitted_at":"2016-03-21T09:05:09Z","abstract_excerpt":"Let $H$ be a Krull monoid with class group $G$. Then $H$ is factorial if and only if $G$ is trivial. Sets of lengths and sets of catenary degrees are well studied invariants describing the arithmetic of $H$ in the non-factorial case. In this note we focus on the set $Ca (H)$ of catenary degrees of $H$ and on the set $\\mathcal R (H)$ of distances in minimal relations. We show that every finite nonempty subset of $\\mathbb N_{\\ge 2}$ can be realized as the set of catenary degrees of a Krull monoid with finite class group. This answers Problem 4.1 of {arXiv:1506.07587}. Suppose in addition that ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06356","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"}