{"paper":{"title":"Functional identities of one variable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Matej Bre\\v{s}ar, \\v{S}pela \\v{S}penko","submitted_at":"2013-07-08T20:29:26Z","abstract_excerpt":"Let $A$ be a centrally closed prime algebra over a characteristic 0 field $k$, and let $q:A\\to A$ be the trace of a $d$-linear map (i.e., $q(x)=M(x,...,x)$ where $M:A^d\\to A$ is a $d$-linear map). If $[q(x),x]=0$ for every $x\\in A$, then $q$ is of the form $q(x) =\\sum_{i=0}^{d} \\mu_i(x)x^i$ where each $\\mu_i$ is the trace of a $(d-i)$-linear map from $A$ into $k$. For infinite dimensional algebras and algebras of dimension $>d^2$ this was proved by Lee, Lin, Wang, and Wong in 1997. In this paper we cover the remaining case where the dimension is $ \\le d^2$. Using this result we are able to han"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2260","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"}