{"paper":{"title":"The system of sets of lengths in Krull monoids under set addition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Alfred Geroldinger (IM), Wolfgang Schmid (LAGA)","submitted_at":"2014-07-08T06:30:05Z","abstract_excerpt":"Let $H$ be a Krull monoid with class group $G$ and suppose that each class contains a prime divisor. Then every element $a \\in H$ has a factorization into irreducible elements, and the set $\\mathsf L (a)$ of all possible factorization lengths is the set of lengths of $a$. We consider the system $\\mathcal L (H) = \\{ \\mathsf L (a) \\mid a \\in H \\}$ of all sets of lengths, and we characterize (in terms of the class group $G$) when $\\mathcal L (H)$ is additively closed under set addition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1967","kind":"arxiv","version":3},"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"}