Narrow Results

Let $\mathcal{R}$ be a ∗-ring with the center 𝒵($\mathcal{R}$) and ℕ be the set of nonnegative integers. In this paper, it is shown that if $\mathcal{R}$ contains a nontrivial self-adjoint idempotent which admits a generalized ∗-Lie higher derivable mapping Δ = {G_n}_n∈ℕ associated with a ∗-Lie higher derivable mapping ℒ = {L_n}_n∈ℕ, then for any X, Y in $\mathcal{R}$ and for each n in ℕ there exists an element Z_X,Y (depending on X and Y) in the center 𝒵($\mathcal{R}$) such that G_n(X + Y ) = G_n(X) + G_n(Y) + Z_X,Y.