### 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 language | English |
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Pages (from-to) | 3099-3108 |

Number of pages | 10 |

Journal | Linear Algebra and Its Applications |

Volume | 436 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2012 May 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Linear Algebra and Its Applications*,

*436*(9), 3099-3108. https://doi.org/10.1016/j.laa.2011.10.014

}

*Linear Algebra and Its Applications*, vol. 436, no. 9, pp. 3099-3108. https://doi.org/10.1016/j.laa.2011.10.014

**Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution.** / Liau, Pao Kuei; Huang, Wei Lu; Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution

AU - Liau, Pao Kuei

AU - Huang, Wei Lu

AU - Liu, Cheng-Kai

PY - 2012/5/1

Y1 - 2012/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84857995413&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857995413&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2011.10.014

DO - 10.1016/j.laa.2011.10.014

M3 - Article

AN - SCOPUS:84857995413

VL - 436

SP - 3099

EP - 3108

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 9

ER -