{"paper":{"title":"Sets of lengths in maximal orders in central simple algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniel Smertnig","submitted_at":"2013-06-04T15:41:51Z","abstract_excerpt":"Let $\\mathcal O$ be a holomorphy ring in a global field $K$, and $R$ a classical maximal $\\mathcal O$-order in a central simple algebra over $K$. We study sets of lengths of factorizations of cancellative elements of $R$ into atoms (irreducibles). In a large majority of cases there exists a transfer homomorphism to a monoid of zero-sum sequences over a ray class group of $\\mathcal O$, which implies that all the structural finiteness results for sets of lengths---valid for commutative Krull monoids with finite class group---hold also true for $R$. If $\\mathcal O$ is the ring of algebraic intege"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0834","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"}