{"paper":{"title":"A characterization of class groups via sets of lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.AC","authors_text":"Alfred Geroldinger (IM), Wolfgang Schmid (LAGA)","submitted_at":"2015-03-16T15:12:43Z","abstract_excerpt":"Let $H$ be a Krull monoid with class group $G$ such that every class contains a prime divisor. Then every nonunit $a \\in H$ can be written as a finite product of irreducible elements. If $a=u\\_1 \\cdot \\ldots \\cdot u\\_k$, with irreducibles $u\\_1, \\ldots u\\_k \\in H$, then $k$ is called the length of the factorization and the set $\\mathsf L (a)$ of all possible $k$ is called the set of lengths of $a$. It is well-known that the system $\\mathcal L (H) = \\{\\mathsf L (a) \\mid a \\in H \\}$ depends only on the class group $G$. In the present paper we study the inverse question asking whether or not the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04679","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"}