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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2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors would like to thank the referee who gave detailed and thoughtful comments to improve this article. Particularly, the arguments of Lemma 4 and Corollary were suggested by the referee, which shorten our original arguments.
This work was supported partially by Tianyuan Fund of China, YNSF of Shanxi and NSF of China.
Notes
Communicated by M. Bresar.