Strong commutativity preserving maps on Lie ideals

Jer Shyong Lin, Cheng-Kai Liu

Research output: Contribution to journalArticle

31 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 languageEnglish
Pages (from-to)1601-1609
Number of pages9
JournalLinear Algebra and Its Applications
Volume428
Issue number7
DOIs
Publication statusPublished - 2008 Apr 1

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Lie Ideal
Commutativity
Chara
Extended Centroid
Prime Ring
Standards

All Science Journal Classification (ASJC) codes

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

Cite this

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Strong commutativity preserving maps on Lie ideals. / Lin, Jer Shyong; Liu, Cheng-Kai.

In: Linear Algebra and Its Applications, Vol. 428, No. 7, 01.04.2008, p. 1601-1609.

Research output: Contribution to journalArticle

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