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

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 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

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*Communications in Algebra*, vol. 41, no. 5, pp. 1636-1646. https://doi.org/10.1080/00927872.2011.649223

**On the Centralizers of Derivations with Engel Conditions.** / Liu, Cheng-Kai; Shiue, Wen Kwei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the Centralizers of Derivations with Engel Conditions

AU - Liu, Cheng-Kai

AU - Shiue, Wen Kwei

PY - 2013/5/1

Y1 - 2013/5/1

N2 - 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, d2 = 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.

AB - 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, d2 = 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.

UR - http://www.scopus.com/inward/record.url?scp=84878133156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878133156&partnerID=8YFLogxK

U2 - 10.1080/00927872.2011.649223

DO - 10.1080/00927872.2011.649223

M3 - Article

AN - SCOPUS:84878133156

VL - 41

SP - 1636

EP - 1646

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 5

ER -