A Result Concerning Additive Mappings in Semiprime Rings

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A Result Concerning Additive Mappings in Semiprime Rings

Fosner, Maja

Mathematica Slovaca, 12/2015, Volume: 65, Issue: 6

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In this paper we prove the following result. Let R be a 2-torsion free semiprime ring and let f : R → R be an additive mapping satisfying the relation f(x)x + x f(x) = 0 for all x ∈ R. In this case f = 0. Any semisimple Banach algebra (for example, C* algebra) is semiprime. Therefore this algebraic result might be of some interest from functional analysis point of view.

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