{"paper":{"title":"The number of atoms in an atomic domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"Paul Pollack, Pete L. Clark, Saurabh Gosavi","submitted_at":"2015-12-16T02:03:20Z","abstract_excerpt":"We study the number of atoms and maximal ideals in an atomic domain with finitely many atoms and no prime elements. We show in particular that for all $m,n \\in \\mathbb{Z}^+$ with $n \\geq 3$ and $4 \\leq m \\leq \\frac{n}{3}$ there is an atomic domain with precisely $n$ atoms, precisely $m$ maximal ideals and no prime elements. The proofs use both commutative algebra and additive number theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05024","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"}