{"paper":{"title":"A Characterization of class groups via sets of lengths {II}","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alfred Geroldinger, Qinghai Zhong","submitted_at":"2015-06-17T07:23:57Z","abstract_excerpt":"Let $H$ be a Krull monoid with finite class group $G$ and suppose that every class contains a prime divisor. If an element $a \\in H$ has a factorization $a=u_1 \\cdot \\ldots \\cdot u_k$ into irreducible elements $u_1, \\ldots, u_k \\in H$, then $k$ is called the length of the factorization and the set $\\mathsf L (a)$ of all possible factorization lengths is the set of lengths of $a$. It is classical that the system $\\mathcal L (H) = \\{ \\mathsf L (a) \\mid a \\in H \\}$ of all sets of lengths depends only on the class group $G$, and a standing conjecture states that conversely the system $\\mathcal L ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05223","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"}