{"paper":{"title":"Power-central polynomials on matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Alexei Kanel-Belov, Louis Rowen, Sergey Malev","submitted_at":"2013-10-06T16:41:52Z","abstract_excerpt":"Any multilinear non-central polynomial $p$ (in several noncommuting variables) takes on values of degree $n$ in the matrix algebra $M_n(F)$ over an infinite field $F$. The polynomial $p$ is called {\\it $\\nu$-central} for $M_n(F)$ if $p^\\nu$ takes on only scalar values, with $k$ minimal such. Multilinear $\\nu$-central polynomials do not exist for any $\\nu$ with $n>3$, thereby answering a question of Drensky. Saltman proved that an arbitrary polynomial\n  $p$ cannot be $\\nu$-central for $M_n(F)$ for $n$ odd unless $n$ is prime; we show for $n$ even, that $\\nu$ must be 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1598","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"}