{"paper":{"title":"Local Selectivity of Orders in Central Simple Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Benjamin Linowitz, Thomas R. Shemanske","submitted_at":"2012-04-11T19:01:58Z","abstract_excerpt":"Let $B$ be a central simple algebra of degree $n$ over a number field $K$, and $L\\subset B$ a strictly maximal subfield. We say that the ring of integers $\\mathcal O_L$ is \"selective\" if there exists an isomorphism class of maximal orders in $B$ no element of which contains $\\mathcal O_L$. Many authors have worked to characterize the degree to which selectivity occurs, first in quaternion algebras, and more recently in higher-rank algebras. In the present work, we consider a local variant of the selectivity problem and applications. \nWe first prove a theorem characterizing which maximal orders"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2526","kind":"arxiv","version":3},"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"}