On the Centralizers of Derivations with Engel Conditions

Cheng-Kai Liu, Wen Kwei Shiue

Research output: Contribution to journal › Article

5 Citations (Scopus)

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, 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.

Original languageEnglish
Pages (from-to)1636-1646
Number of pages11
JournalCommunications in Algebra
Volume41
Issue number5
DOIs
Publication statusPublished - 2013 May 1

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Extended Centroid
Non-commutative Rings
Prime Ring
Centralizer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Liu, Cheng-Kai ; Shiue, Wen Kwei. / On the Centralizers of Derivations with Engel Conditions. In: Communications in Algebra. 2013 ; Vol. 41, No. 5. pp. 1636-1646.
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Liu, C-K & Shiue, WK 2013, 'On the Centralizers of Derivations with Engel Conditions', 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.

In: Communications in Algebra, Vol. 41, No. 5, 01.05.2013, p. 1636-1646.

Research output: Contribution to journal › Article

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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.

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Liu C-K, Shiue WK. On the Centralizers of Derivations with Engel Conditions. Communications in Algebra. 2013 May 1;41(5):1636-1646. https://doi.org/10.1080/00927872.2011.649223

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