{"paper":{"title":"Representation of Cyclotomic Fields and Their Subfields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A.K.Lal, A.Satyanarayana Reddy, Shashank K Mehta","submitted_at":"2011-06-09T07:48:36Z","abstract_excerpt":"Let $\\K$ be a finite extension of a characteristic zero field $\\F$. We say that the pair of $n\\times n$ matrices $(A,B)$ over $\\F$ represents $\\K$ if $\\K \\cong \\F[A]/< B >$ where $\\F[A]$ denotes the smallest subalgebra of $M_n(\\F)$ containing $A$ and $< B >$ is an ideal in $\\F[A]$ generated by $B$. In particular, $A$ is said to represent the field $\\K$ if there exists an irreducible polynomial $q(x)\\in \\F[x]$ which divides the minimal polynomial of $A$ and $\\K \\cong \\F[A]/< q(A) >$. In this paper, we identify the smallest circulant-matrix representation for any subfield of a cyclotomic field. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1727","kind":"arxiv","version":2},"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"}