|
|
| |
| On Regular Power-Substitution |
| |
Citation： |
Huanyin CHEN.On Regular Power-Substitution[J].Chinese Annals of Mathematics B,2009,30(3):221~230 |
| Page view： 1646
Net amount： 1161 |
Authors： |
Huanyin CHEN; |
Foundation： |
the grant of Hangzhou Normal University (No. 200901). |
|
|
| Abstract： |
The necessary and sufficient conditions under which a ring satisfies
regular power-substitution are investigated. It is shown that a ring
$R$ satisfies regular power-substitution if and only if $a\ov\sim b$
in $R$ implies that there exist $n\in\BN$ and a $U\in\GL_n(R)$ such
that $aU=Ub$ if and only if for any regular $x\in R$ there exist
$m,n\in\BN$ and $U\in\GL_n(R)$ such that $x^mI_n=x^mUx^m$, where
$a\ov\sim b$ means that there exists $x,y,z\in R$ such that $a=ybx$,
$b=xaz$ and $x=xyx=xzx$. It is proved that every directly finite
simple ring satisfies regular power-substitution. Some applications
for stably free $R$-modules are also obtained. |
Keywords： |
Regular power-substitution, Regular power-cancellation, Stably free module |
Classification： |
16E50, 19B10 |
|
|
Download PDF Full-Text
|
|
|
|
