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 |
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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