| A Note on Commutators with Power Central Values on Lie Ideals |
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| 作者姓名： | Yu WANG Hong YOU |
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| 作者单位： | [1]College of Mathematics, Jilin Normal University, Siping 136000, P. R. China [2]College of Sciences, Harbin Institute of Technology, Harbin 150001, P. R. China |
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| 基金项目： | Partially supported by China Postdoctoral Science Foundation Acknowledgements The authors would for valuable suggestions which help clarify like to express their sincere thanks to the referees the whole paper. The first author expresses his sincere gratitude to Dr. Gao Yan for her enthusiastic encouragement, energetical support and unselfish help for many years. |
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| 摘 要： | This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis＇s results.
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| 关 键 词： | 素环 半素环 数学分析 环论 |
| 收稿时间： | 2004-08-11 |
| 修稿时间： | 2004-08-112005-07-27 |
A Note on Commutators with Power Central Values on Lie Ideals |
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| Yu WANG Hong YOU.A Note on Commutators with Power Central Values on Lie Ideals[J].Acta Mathematica Sinica,2006,22(6):1715-1720. |
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| Authors: | Yu Wang Hong You |
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| Institution: | (1) College of Mathematics, Jilin Normal University, Siping 136000, P. R. China;(2) College of Sciences, Harbin Institute of Technology, Harbin 150001, P. R. China |
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| Abstract: | This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that d(u), u] n is central, for all u ∈¸ L, then R must satisfy s 4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis’s results. |
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| Keywords: | prime ring semiprime ring lie ideal derivation |
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