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| ON SUBGROUPS OF GL_2 OVER A CLASS OF NON-COMMUTATIVE RINGS WHICH ARE NORMALIZED BY ELEMENTARY MATRICES |
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Citation： |
You Hong.ON SUBGROUPS OF GL_2 OVER A CLASS OF NON-COMMUTATIVE RINGS WHICH ARE NORMALIZED BY ELEMENTARY MATRICES[J].Chinese Annals of Mathematics B,1993,14(4):507~514 |
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Net amount： 720 |
Authors： |
You Hong; |
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| Abstract： |
Let R be an associative ring with 1 and $Y \ne R$ a quasi-ideal of R. Set $T_2(R,Y)={diag(u,v)a^{1,2}b^{2,1}c^{1,2}:a+c,b\in Y,u,v\in GL_1R,and v^{-1}au-a,uav^{-1}-a\in Y for all a\in R}$.It is proved that if R satisfies 2-fold condition, then $[E_2R,T_2(R,Y)]\subset E_2(R,Y)\subset T_2(R,Y)$; and if R satisfies 6-fold condition, then $E_2(R,Y)=[E_2R,E_2(R,Y)]=[E_2R,T_2(R,Y)]$ and the sandwich theorem holds. |
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