{"paper":{"title":"The lattice of primary ideals of orders in quadratic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"Giulio Peruginelli, Paolo Zanardo","submitted_at":"2015-03-20T10:17:06Z","abstract_excerpt":"Let $O$ be an order in a quadratic number field $K$ with ring of integers $D$, such that the conductor $\\mathfrak F = f D$ is a prime ideal of $O$, where $f\\in\\mathbb Z$ is a prime. We give a complete description of the $\\mathfrak F$-primary ideals of $O$. They form a lattice with a particular structure by layers; the first layer, which is the core of the lattice, consists of those $\\mathfrak F$-primary ideals not contained in $\\mathfrak F^2$. We get three different cases, according to whether the prime number $f$ is split, inert or ramified in $D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06033","kind":"arxiv","version":4},"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"}