### Abstract

Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ^{2} = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.

Original language | English |
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Pages (from-to) | 1601-1609 |

Number of pages | 9 |

Journal | Linear Algebra and Its Applications |

Volume | 428 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2008 Apr 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*,

*428*(7), 1601-1609. https://doi.org/10.1016/j.laa.2007.10.006

}

*Linear Algebra and Its Applications*, vol. 428, no. 7, pp. 1601-1609. https://doi.org/10.1016/j.laa.2007.10.006

**Strong commutativity preserving maps on Lie ideals.** / Lin, Jer Shyong; Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong commutativity preserving maps on Lie ideals

AU - Lin, Jer Shyong

AU - Liu, Cheng-Kai

PY - 2008/4/1

Y1 - 2008/4/1

N2 - Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.

AB - Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R → A is called strong commutativity preserving (SCP) on R if [f (x), f (y)] = [x, y] for all x, y ∈ R. In this paper we show that if f is SCP on R, then there exist λ ∈ C, λ2 = 1 and an additive map μ : R → Z (A) such that f (x) = λ x + μ (x) for all x ∈ R where C is the extended centroid of A, unless charA = 2 and A satisfies the standard identity of degree 4.

UR - http://www.scopus.com/inward/record.url?scp=38849151577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38849151577&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2007.10.006

DO - 10.1016/j.laa.2007.10.006

M3 - Article

AN - SCOPUS:38849151577

VL - 428

SP - 1601

EP - 1609

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 7

ER -