# 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 language English 14-23 10 Linear Algebra and Its Applications 432 1 https://doi.org/10.1016/j.laa.2009.06.036 Published - 2010 Jan 1

### Fingerprint

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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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.",
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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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AU - Liu, Cheng-Kai

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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.

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