{"paper":{"title":"On the Infinitude of Prime Ideals in Dedekind Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2014-03-14T01:50:13Z","abstract_excerpt":"Let $R$ be an infinite Dedekind domain with at most finitely many units, and let $K$ denote its field of fractions. We prove the following statement. If $L/K$ is a finite Galois extension of fields and $\\mathcal{O}$ is the integral closure of $R$ in $L$, then $\\mathcal{O}$ contains infinitely many prime ideals. In particular, if $\\mathcal{O}$ is further a unique factorization domain, then $\\mathcal{O}$ contains infinitely many non-associate prime elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3473","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"}