• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.331-343
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• 2024

Let ℜ be a *-algebra with unity I and a nontrivial projection P₁. In this paper, we show that under certain restrictions if a map ψ : ℜ → ℜ satisfies $$\Psi(S_1{\diamond}S_2{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n)=\sum_{k=1}^nS_1{\diamond}S_2{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{k-1}{\diamond}{\Psi}(S_k){\diamond}S_{k+1}{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n$$ for all S_n-2, S_n-1, S_n ∈ ℜ and S_i = I for all i ∈ {1, 2, . . . , n - 3}, where n ≥ 3, then ψ is an additive *-derivation.