{"paper":{"title":"Semistar operations on Dedekind domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jesse Elliott","submitted_at":"2011-10-10T00:53:34Z","abstract_excerpt":"We give an explicit description of the lattice $\\Semistar(D)$ of all semistar operations on any Dedekind domain $D$ from its set $\\Max(D)$ of maximal ideals. This descpription is constructive if $\\Max(D)$ is finite. As a corollary we show that $2^{{n \\choose [n/2]}} \\leq |\\Semistar(D)| \\leq 2^{2^n}$ if $n = |\\Max(D)|$ is finite; we compute $|\\Semistar(D)|$ if $|\\Max(D)| \\leq 7$; and we show that if $\\Max(D)$ is infinite then $\\Semistar(D)$ has cardinality $2^{2^{|\\Max(D)|}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1898","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"}