Strong commutativity preserving maps in prime rings with involution

Jer Shyong Lin, Cheng-Kai Liu

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let A be a prime ring of characteristic not 2, with center Z A and with involution. Let S be the set of symmetric elements of A. Suppose that f : S → A is an additive map such that [f (x), f (y)] = [x, y] for all x, y ∈ S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ : S → Z (A) such that f (x) = x + μ (x) for all x ∈ S or f (x) = - x + μ (x) for all x ∈ S.

Original languageEnglish
Pages (from-to)14-23
Number of pages10
JournalLinear Algebra and Its Applications
Volume432
Issue number1
DOIs
Publication statusPublished - 2010 Jan 1

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Prime Ring
Commutativity
Involution
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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Strong commutativity preserving maps in prime rings with involution. / Lin, Jer Shyong; Liu, Cheng-Kai.

In: Linear Algebra and Its Applications, Vol. 432, No. 1, 01.01.2010, p. 14-23.

Research output: Contribution to journalArticle

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