On the Centralizers of Derivations with Engel Conditions

Cheng-Kai Liu; Wen Kwei Shiue

doi:10.1080/00927872.2011.649223

On the Centralizers of Derivations with Engel Conditions

Cheng-Kai Liu, Wen Kwei Shiue

Department of Mathematics

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 language	English
Pages (from-to)	1636-1646
Number of pages	11
Journal	Communications in Algebra
Volume	41
Issue number	5
DOIs	https://doi.org/10.1080/00927872.2011.649223
Publication status	Published - 2013 May 1

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All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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

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Access to Document

10.1080/00927872.2011.649223