Let ℛ be a unital *-ring with the unit I. Assume that ℛ contains a symmetric idempotent P such that AℛP = 0 implies A = 0 and Aℛ(I − P) = 0 implies A = 0. We prove that if ϕ: ℛ → ℛ is a nonlinear skew commuting map, then there exists an element Z ∈ \( \mathcal{Z} \)S(ℛ) such that ϕ X) = ZX for all X ∈ ℛ, where \( \mathcal{Z} \)S(ℛ) is the symmetric center of ℛ. As an application, we obtain the form of nonlinear skew commuting maps on the factors.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 6, pp. 826–831, June, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i6.801.
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Kong, L., Zhang, J. Nonlinear Skew Commuting Maps on *-Rings. Ukr Math J 74, 946–952 (2022). https://doi.org/10.1007/s11253-022-02108-z
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DOI: https://doi.org/10.1007/s11253-022-02108-z