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Nonlinear ξ-Jordan triple *-derivation on prime *-algebras

Rocky Mountain Journal of Mathematics, 2022
Let A be a prime ∗-algebra and let ξ ∈ C \ {0,±1}. In this paper, it is proved that a mapping φ : A → A satisfies φ(A ξ B ξ C) = φ(A) ξ B ξ C +A ξ φ(B) ξ C +A ξ B ξ φ(C) for all A,B,C ∈ A if and only if φ is an additive ∗-derivation and φ(ξA) = ξφ(A) for
Fangjuan Zhang
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Nonlinear anti-commuting maps of unital algebras with idempotents

International Mathematical Forum, 2019
Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-
Liqin Feng, X. Qi
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