{"paper":{"title":"D\\'ecomposition effective de Jordan-Chevalley et ses retomb\\'ees en enseignement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Danielle Couty (IMT), Jean Esterle (IMB), Rachid Zarouf (LATP)","submitted_at":"2011-03-25T16:32:04Z","abstract_excerpt":"The purpose of this paper is to point the effectiveness of the Jordan-Chevalley decomposition, i.e. the decomposition of a square matrix $U$ with coefficients in a field $k$ containing the eigenvalues of $U$ as a sum $U=D+N,$ where $D$ is a diagonalizable matrix and $N$ a nilpotent matrix which commutes with $D.$ The most general version of this decomposition shows that every separable element $u$ of a $k$-algebra $A$ can be written in a unique way as a sum $u=d+n,$ where $d \\in A$ is absolutely semi-simple and where $n\\in A$ is nilpotent and commutes with $d.$ In fact an algorithm, due to C. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5020","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"}