NOTES ON LIE IDEALS OF SIMPLE ARTINIAN RINGS

被引:0
|
作者
Ariannejad, M. [1 ]
Emami, M. [1 ]
机构
[1] Univ Zanjan, Dept Math, Zanjan, Iran
关键词
Simple ring; division ring; Lie ideal; Lie ring;
D O I
10.1142/S0219498813500382
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let R be a ring. If we replace the original associative product of R with their canonic Lie product, or [a, b] = ab - ba for every a, b in R, then R would be a Lie ring. With this new product the additive commutator subgroup of R or [R, R] is a Lie subring of R. Herstein has shown that in a simple ring R with characteristic unequal to 2, any Lie ideal of R either is contained in Z(R), the center of R or contains [R, R]. He also showed that in this situation the Lie ring [R, R]/Z[R, R] is simple. We give an alternative matrix proof of these results for the special case of simple artinian rings and show that in this case the characteristic condition can be more restricted.
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页数:6
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