{"paper":{"title":"The set of minimal distances in Krull monoids","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.AC","authors_text":"Alfred Geroldinger, Qinghai Zhong","submitted_at":"2014-04-10T16:34:06Z","abstract_excerpt":"Let $H$ be a Krull monoid with finite class group $G$. Then every non-unit $a \\in H$ can be written as a finite product of atoms, say $a=u_1 \\cdot \\ldots \\cdot u_k$. The set $\\mathsf L (a)$ of all possible factorization lengths $k$ is called the set of lengths of $a$. If $G$ is finite, then there is a constant $M \\in \\mathbb N$ such that all sets of lengths are almost arithmetical multiprogressions with bound $M$ and with difference $d \\in \\Delta^* (H)$, where $\\Delta^* (H)$ denotes the set of minimal distances of $H$. We show that $\\max \\Delta^* (H) \\le \\max \\{\\exp (G)-2, \\mathsf r (G)-1\\}$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2873","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"}