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Let A and B be two prime ∗-rings. Let Φ : A → B be a bijective and satisfies Φ(A •λ P •λ P ) = Φ(A) •λ Φ(P ) •λ Φ(P ), for all A ∈ A and P ∈ {I, P1, I − P1} where P1 is a projection in A. The operation •λ between two arbitrary elements S and T in A is defined as S •λ T = ST + λTS ∗ for λ ∈ {−1, 1}. Then, if Φ(I) is projection, we show that Φ is additive.

Additivity of maps preserving triple product on *-ring