Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution

Pao Kuei Liau, Wei Lu Huang, Cheng-Kai Liu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let A be a prime ring of characteristic not 2, with involution, with center Z(A) and with skew elements K. Suppose that f:K→A is a map satisfying [f(x),f(y)]=[x,y] for all x,y∈K. Then there exists a map μ:K→Z(A) such that f(x)=x+μ(x) for all x∈K or f(x)=-x+μ(x) for all x∈K except when A is an order in a 4, 9 or 16-dimensional central simple algebra.

Original languageEnglish
Pages (from-to)3099-3108
Number of pages10
JournalLinear Algebra and Its Applications
Volume436
Issue number9
DOIs
Publication statusPublished - 2012 May 1

Fingerprint

Prime Ring
Commutativity
Involution
Skew
Central Simple Algebra
Algebra

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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abstract = "Let A be a prime ring of characteristic not 2, with involution, with center Z(A) and with skew elements K. Suppose that f:K→A is a map satisfying [f(x),f(y)]=[x,y] for all x,y∈K. Then there exists a map μ:K→Z(A) such that f(x)=x+μ(x) for all x∈K or f(x)=-x+μ(x) for all x∈K except when A is an order in a 4, 9 or 16-dimensional central simple algebra.",
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Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution. / Liau, Pao Kuei; Huang, Wei Lu; Liu, Cheng-Kai.

In: Linear Algebra and Its Applications, Vol. 436, No. 9, 01.05.2012, p. 3099-3108.

Research output: Contribution to journalArticle

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