Strong commutativity preserving maps on Lie ideals |
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Authors: | Jer-Shyong Lin |
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Institution: | a Department of Information Management, Yuanpei University, Hsinchu 300, Taiwan b Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan |
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Abstract: | Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f:R→A is called strong commutativity preserving (SCP) on R if f(x),f(y)]=x,y] for all x,y∈R. In this paper we show that if f is SCP on R, then there exist λ∈C, λ2=1 and an additive map μ:R→Z(A) such that f(x)=λx+μ(x) for all x∈R where C is the extended centroid of A, unless charA=2 and A satisfies the standard identity of degree 4. |
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Keywords: | 16R50 16N60 16U80 |
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