### Abstract

Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

Original language | English |
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Pages (from-to) | 1236-1242 |

Number of pages | 7 |

Journal | Linear Algebra and Its Applications |

Volume | 430 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Feb 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*,

*430*(4), 1236-1242. https://doi.org/10.1016/j.laa.2008.10.022

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*Linear Algebra and Its Applications*, vol. 430, no. 4, pp. 1236-1242. https://doi.org/10.1016/j.laa.2008.10.022

**On generalized Lie derivations of Lie ideals of prime algebras.** / Liao, Ping Bao; Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On generalized Lie derivations of Lie ideals of prime algebras

AU - Liao, Ping Bao

AU - Liu, Cheng-Kai

PY - 2009/2/1

Y1 - 2009/2/1

N2 - Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

AB - Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.

UR - http://www.scopus.com/inward/record.url?scp=58049192816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049192816&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2008.10.022

DO - 10.1016/j.laa.2008.10.022

M3 - Article

AN - SCOPUS:58049192816

VL - 430

SP - 1236

EP - 1242

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 4

ER -