{"paper":{"title":"Improved algorithms for splitting full matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"\\'Ad\\'am D. Lelkes, G\\'abor Ivanyos, Lajos R\\'onyai","submitted_at":"2012-11-06T19:35:32Z","abstract_excerpt":"Let $\\K$ be an algebraic number field of degree $d$ and discriminant $\\Delta$ over $\\Q$. Let $\\A$ be an associative algebra over $\\K$ given by structure constants such that $\\A\\cong M_n(\\K)$ holds for some positive integer $n$. Suppose that $d$, $n$ and $|\\Delta|$ are bounded. In a previous paper a polynomial time ff-algorithm was given to construct explicitly an isomorphism $\\A \\rightarrow M_n(\\K)$.\n  Here we simplify and improve this algorithm in the cases $n\\leq 43$, $\\K=\\Q$, and $n=2$, with $\\K=\\Q(\\sqrt{-1})$ or $\\K=\\Q(\\sqrt{-3})$. The improvements are based on work by Y. Kitaoka and R. Co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1356","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"}