### Abstract

Let R be a noncommutative prime ring and d, δ two nonzero derivations of R. If δ([d(x), x]_{n}) = 0 for all x ∈ R, then char R = 2, d^{2} = 0, and δ = αd, where α is in the extended centroid of R. As an application, if char R ≠ 2, then the centralizer of the set {[d(x), x]_{n} {pipe} x ∈ R} in R coincides with the center of R.

Original language | English |
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Pages (from-to) | 1636-1646 |

Number of pages | 11 |

Journal | Communications in Algebra |

Volume | 41 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2013 May 1 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Liu, C-K., & Shiue, W. K. (2013). On the Centralizers of Derivations with Engel Conditions.

*Communications in Algebra*,*41*(5), 1636-1646. https://doi.org/10.1080/00927872.2011.649223