Nonlinear Strong Commutativity Preserving Maps on Prime Rings |
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| Authors: | Xiaofei Qi Jinchuan Hou |
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| Institution: | 1. Department of Mathematics , Shanxi University , Taiyuan, China qixf1980@126.com;3. Department of Mathematics , Shanxi University , Taiyuan, China;4. Department of Mathematics , Taiyuan University of Technology , Taiyuan, China |
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| Abstract: | Let 𝒜 be a unital prime ring containing a nontrivial idempotent P. Assume that Φ: 𝒜 → 𝒜 is a nonlinear surjective map. It is shown that Φ preserves strong commutativity if and only if Φ has the form Φ(A) = αA + f(A) for all A ∈ 𝒜, where α ∈ {1, ?1} and f is a map from 𝒜 into 𝒵(𝒜). As an application, a characterization of nonlinear surjective strong commutativity preserving maps on factor von Neumann algebras is obtained. |
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| Keywords: | Factor von Neumann algebras Nonlinear strong commutativity preserving maps Prime rings |
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