Chinese Quarterly Journal of Mathematics ›› 2020, Vol. 35 ›› Issue (2): 179-185.doi: 10.13371/j.cnki.chin.q.j.m.2020.02.005

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Left Annihilator of Power Values with Derivations on Lie Ideals in Prime Rings

  

  1. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China
  • Received:2019-12-20 Online:2020-06-30 Published:2020-09-03
  • About author:HUANG Shu-liang(1981-), male, native of Weifang, Shandong, a professor of Chuzhou University, engages in rings and algebras.
  • Supported by:
    Supported by Anhui Natural Science Foundation(1808085MA14;1908085MA03) and the Key University Science Research Project of Anhui Province(KJ2018A0433)

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Abstract:

Let R be a prime ring with characteristic di®erent from two, d a derivation of R, L a noncentral Lie ideal of R, and a \in R. In the present paper it is showed that if 

a(d(u^m)\pm u^m)^n=0

for all u \in L, where m; n are fixed positive integers, then a = 0 unless R satisfies s4, the standard polynomial identity in four variables.

Key words: Derivation, Extended centroid, Lie ideal, Prime ring

CLC Number: 

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