Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (4): 628-632.

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Some Conditions of Central Lie Ideal

  

  1. 1. Department of Mathematics, Chuzhou University2. School of Mathematics and Computer Science, Nanjing Normal University
  • Received:2006-06-05 Online:2009-12-30 Published:2023-06-21
  • About author:HUANG Shu-liang(1981-), male, native of Changyi, Shandong, a lecturer of Chuzhou University, M.S.D., engages in ring theory; FU Shi-tai(1962-), male, native of Huai'an, Jiangsu, an associate professor of Nanjing Normal University, Ph.D., engages in Hopf algebra.
  • Supported by:
     Supported by the Natural Science Research Item of Anhui Province College(KJ2008B013);

Abstract: Let di(1≤i≤n), δ123 be nonzero derivations of a prime ring R with charR≠2.Suppose that U is a Lie ideal such that u2∈U for all u∈U. In this paper, we prove that U Z(R) when one of the following holds: (1) d1(x1)d2(x2),...,dn(xn)∈Z(R)(2)δ3(y)δ1(x)=δ2(x)δ3(y). Further, if U is a Lie ideal and a subring then (3)δ1(x)δ2(y)+δ2(x)δ1(y)∈Z(R) for all xi,x,y∈U. 

Key words:  prime ring, Lie ideal, derivation

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