|
|
| |
| THE STRUCTURE OF ORTHOGONAL GROUPS OVER ARBITRARY COMMUTATIVE RINGS |
| |
Citation： |
Li Fuan.THE STRUCTURE OF ORTHOGONAL GROUPS OVER ARBITRARY COMMUTATIVE RINGS[J].Chinese Annals of Mathematics B,1989,10(3):341~350 |
| Page view： 917
Net amount： 798 |
Authors： |
Li Fuan; |
Foundation： |
Projects supported by the Science Fund of the Chinese Acsdemy of Sciences |
|
|
| Abstract： |
Let $R$ be an arbitrary commutative ring, and $n$ an integer $\[ \ge 3\]$. It is proved for any ideal J of $R$ that
$$\[\begin{array}{*{20}{c}}
{E{O_{2n}}(R,J) = [E{O_{2n}}(R),E{O_{2n}}(J)] = [E{O_{2n}}(R),E{O_{2n}}(R,J)]}\{ = [E{O_{2n}}(R),{O_{2n}}(R,J)] = [{O_{2n}}(R),E{O_{2n}}(R,J)]}
\end{array}\]$$
In particular, $\[{E{O_{2n}}(R,J)}\]$ is a normal subgroup of $\[{{O_{2n}}(R)}\]$. Furthermore, the problem of normal subgroups of $\[{{O_{2n}}(R)}\]$ has an affirmative solution if and only if $\[aB \cap Ann(2) = {a^2}Ann(2)\]$ for each $a$ in $R$. In particular, if 2 is not a zero divisor in R, then the problem of normal subgroups of $\[{{O_{2n}}(R)}\]$ has an affirmative solution. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
