### 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 language | English |
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Pages (from-to) | 14-23 |

Number of pages | 10 |

Journal | Linear Algebra and Its Applications |

Volume | 432 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Jan 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

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*Linear Algebra and Its Applications*, vol. 432, no. 1, pp. 14-23. https://doi.org/10.1016/j.laa.2009.06.036

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong commutativity preserving maps in prime rings with involution

AU - Lin, Jer Shyong

AU - Liu, Cheng-Kai

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70449586846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449586846&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2009.06.036

DO - 10.1016/j.laa.2009.06.036

M3 - Article

AN - SCOPUS:70449586846

VL - 432

SP - 14

EP - 23

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1

ER -