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Title: Strong Commutativity Preserving Maps on Lie Ideals
Authors: Lin, Jer-Shyong;Liu, Cheng-Kai
Contributors: 數學系
Keywords: Prime ring;Lie ideal;Strong commutativity preserving
Date: 2008-04
Issue Date: 2013-01-07T01:43:38Z
Publisher: Elsevier
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.
Relation: Linear Algebra and its Applications, 428(7): 1601-1609
Appears in Collections:[math] Periodical Articles

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