{"paper":{"title":"Jordan product determined points in matrix algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"Yang Wenlei, Zhu Jun","submitted_at":"2011-11-17T14:23:22Z","abstract_excerpt":"Let $M_n(R)$ be the algebra of all $n\\times n$ matrices over a unital commutative ring $R$ with 6 invertible. We say that $A\\in M_n(R)$ is a Jordan product determined point if for every $R$-module $X$ and every symmetric $R$-bilinear map $\\{\\cdot, \\cdot\\}$ : $M_n(R)\\times M_n(R)\\to X$ the following two conditions are equivalent: (i) there exists a fixed element $w\\in X$ such that $\\{x,y\\}=w$ whenever $x\\circ y=A$, $x,y\\in M_n(R)$; (ii) there exists an $R$-linear map $T:M_n(R)^2\\to X$ such that $\\{x,y\\}=T(x\\circ y)$ for all $x,y\\in M_n(R)$. In this paper, we mainly prove that all the matrix uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4108","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"}