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 | |
| Publication status | Published - 2013 May 1 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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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