### Abstract

Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]_{1} = [x, y] = xy − yx for x, y ∈ R and inductively [x, y]_{k} = [[x, y]_{k−1}, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]_{k} = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ⊆ M_{2}(F), the 2 × 2 matrix ring over a field F.

Original language | English |
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Pages (from-to) | 898-911 |

Number of pages | 14 |

Journal | Communications in Algebra |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 Feb 1 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Chou, M. C., & Liu, C-K. (2016). Annihilators of Skew Derivations with Engel Conditions on Lie Ideals.

*Communications in Algebra*,*44*(2), 898-911. https://doi.org/10.1080/00927872.2014.990028