Jordan product determined points in matrix algebras
نویسندگان
چکیده
Let Mn(R) be the algebra of all n×n matrices over a unital commutative ring R with 6 invertible. We say that A ∈ Mn(R) is a Jordan product determined point if for every R-module X and every symmetric R-bilinear map {·, ·} : Mn(R)×Mn(R) → X the following two conditions are equivalent: (i) there exists a fixed element w ∈ X such that {x, y} = w whenever x ◦ y = A, x, y ∈ Mn(R); (ii) there exists an R-linear map T : Mn(R) → X such that {x, y} = T (x ◦ y) for all x, y ∈ Mn(R). In this paper, we mainly prove that all matrix units are Jordan product determined points in Mn(R) when n ≥ 3. In addition, we get some corollaries by applying the main results. AMS subject classifications: 15A86, 47L05
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