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## Lie structures of [S,S]

WANG Ping hua (Dept.Math.,Quanzhou Teachers College,Quanzhou 362000,Fujian,China)
Let R be a simple associative ring with an involution and Z the center of R.Let S be the set of all symmetric elements in R and K the set of all skew symmetric elements in R.The following results:(1) If the dimension of R as a vector space over Z is larger than 4,then [S,S]=[K,K] and [S,S] =R;(2) If R is with the first involution,and the dimension of R as a vector space over Z is larger than 16,then [S,S]is a simple Lie ring,and [[S,S],[S,S]]=[S,S];(3) If R is with the second involution,and the dimension of R as a vector space over Z is not equal to 4,and the character of R is not equal to 2,then UZ or U=[S,S] for any Lie ideal U of [S,S] are proved.
【CateGory Index】： O153.3
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 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 FU Cheng-hua,CUI Dian-jun(Fushun Teachers College,Fushun 113006,China);Commutativity of associative rings which meets [s,m(i),n(j)] center condition[J];Journal of Anshan University of Science and Technology;2006-06 2 YANG Wen qi (Dept.Math.,Baoji Coll.Arts & Sci.,Baoji 721007,Shaanxi China);Some results of semi-prime ideal of the ring[J];Journal of Baoji College of Arts and Science(Natural Science Edition);2002-02 3 CUI Dian-jun,FU Cheng-hua(Department of Mathematics,Fushun Teachers College,Fushun 113006,Liaoning,China);Commutativity of a class of associative rings[J];Journal of Baoji University of Arts and Sciences(Natural Science Edition);2009-02 4 Liu Shaoxue(Department of Mathematics);STRUCTURE OF ARTINIAN GRADED RINGS[J];Journal of Beijing Normal University(Natural Science);1989-03 5 Zhu Bin (Department of Mathematics, Beijing Normal University, University, 100875,Beijing, China);GRADED PRIMITIVE RINGS AND KAPLANSKY THEOREM[J];JOURNAL OF BEIJING NORMAL UNIVERSITY(NATURAL SCIENCE);1998-01 6 Meng Xiaoqing(Department of Mathematics,Beijing Normal University,100875,Beijing,PRCj;IDEMPOTENTS,RETRACTS AND FIXED-POINTS[J];JOURNAL OF BEIJING NORMAL UNIVERSITY;1994-02 7 Feng Lianggui(Dept. of Math. of Nanjing University,Nanjing 210008);The Injective Radical of Modules[J];Journal of Jiangxi Normal University (Natural Sciences Edition);1994-02 8 WANG Gong-qiang,ZHANG Xi-gou,LIU Chun(Institute of Mathematics and Informatics,Jiangxi Normal University, Nanchang 330022,China);The Idempotents of Certain Hecke Algebras[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2009-02 9 Chen Peici (Department of Mathematics,Jiangxi Normal University,Nanchang 330027);The f regular Radicals of the Semirings with Reversible Addition[J];JOURNAL OF JIANGXI NORMAL UNIVERSITY (NATURAL SCIENCES EDITION);1997-01 10 ZHU Ping (Department of Computation Science & Information Communication, Southern Yangtze University,Wuxi 214036 China);The structure and the numbers of the cyclic subsemigroups and the construction of the quasi-ring[J];Pure and Applied Mathematics;2002-03
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