{"paper":{"title":"The Minimal Degree Standard Identity on $M_nE^2$ and $M_nE^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Barbara Anna Bal\\'azs, Szabolcs M\\'esz\\'aros","submitted_at":"2019-01-21T21:18:05Z","abstract_excerpt":"We prove an Amitsur--Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of $n \\times n$ matrices over the $m$-generated Grassmann algebra is at least $2\\left\\lfloor\\frac{m}{2}\\right\\rfloor+4n-4$ for all $n,m\\geq 2$ and this bound is sharp for $m=2,3$ and any $n\\geq 2$. The arguments are purely combinatorial, based on computing sums of signs corresponding to Eulerian trails in directed graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07085","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"}