On the Centralizers of Derivations with Engel Conditions |
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| Authors: | Cheng-Kai Liu Wen-Kwei Shiue |
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| Institution: | 1. Department of Mathematics , National Changhua University of Education , Changhua , Taiwan ckliu@cc.ncue.edu.tw;3. Department of Computer Science , Dahan Institute of Technology , Hualien , Taiwan |
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| 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 | x ∈ R} in R coincides with the center of R. |
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| Keywords: | Centralizer Derivation Prime ring |
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