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 UZ or U=[S,S] for any Lie ideal U of [S,S] are proved.
【CateGory Index】：
O153.3


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