### 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 |
---|---|

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

}

*Communications in Algebra*, vol. 44, no. 2, pp. 898-911. https://doi.org/10.1080/00927872.2014.990028

**Annihilators of Skew Derivations with Engel Conditions on Lie Ideals.** / Chou, Ming Chu; Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Annihilators of Skew Derivations with Engel Conditions on Lie Ideals

AU - Chou, Ming Chu

AU - Liu, Cheng-Kai

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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 ⊆ M2(F), the 2 × 2 matrix ring over a field F.

AB - 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 ⊆ M2(F), the 2 × 2 matrix ring over a field F.

UR - http://www.scopus.com/inward/record.url?scp=84955489044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955489044&partnerID=8YFLogxK

U2 - 10.1080/00927872.2014.990028

DO - 10.1080/00927872.2014.990028

M3 - Article

AN - SCOPUS:84955489044

VL - 44

SP - 898

EP - 911

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 2

ER -