Strong commutativity preserving maps on Lie ideals

Jer Shyong Lin; Cheng Kai Liu

doi:10.1016/j.laa.2007.10.006

Strong commutativity preserving maps on Lie ideals

Jer Shyong Lin, Cheng Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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) = λ x + 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.

Original language	English
Pages (from-to)	1601-1609
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	7
DOIs	https://doi.org/10.1016/j.laa.2007.10.006
Publication status	Published - 2008 Apr 1

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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AB - 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) = λ x + 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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