Zhaofang Bai, Shuanping Du, Jinchuan Hou
Abstract
Let ℛ be a prime ring with 1 containing a nontrivial idempotent E, and let ℛ′ be another prime ring. If Φ:ℛ → ℛ′ is a multiplicative Lie isomorphism, then Φ(T + S) = Φ(T) + Φ(S) + Z′ T,S for all T, S ∈ ℛ, where Z′ T,S is an element in the center 𝒵′ of ℛ′ depending on T and S.
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Let ℛ be a prime ring with 1 containing a nontrivial idempotent E, and let ℛ′ be another prime ring. If Φ:ℛ → ℛ′ is a multiplicative Lie isomorphism, then Φ(T + S) = Φ(T) + Φ(S) + Z′ T,S for all T, S ∈ ℛ, where Z′ T,S is an element in the center 𝒵′ of ℛ′ depending on T and S.
Key concepts: Mathematics, Prime ring, Multiplicative function, Isomorphism (crystallography), Prime (order theory), Idempotence, Ring (chemistry), Pure mathematics