Let A and B be two prime ∗-algebras. Let Φ : A → B be a bijective and satisfies Φ(A • B • C) = Φ(A) • Φ(B) • Φ(C), for all A,B ∈ A where A • B = A∗B + BA∗. Then, Φ is additive. Moreover, if Φ(I) is idempotent then we show that Φ is R-linear ∗-isomorphism.
