→ recorriendo :感謝 09/27 23:45
推 recorriendo :請問s=a_(n-1)r^(n-1)+...a_1r+a_0怎麼得到的? 09/28 00:27
→ recorriendo :懂了 謝謝 09/28 01:00
※ 引述《recorriendo (孟新)》之銘言：
: If R is a finite dimensional algebra over a field k and if rs = 1, show
: that sr = 1. Deduce that if R contains no zero-divisors, then every non-zero
: element of R has a two sided inverse, that is, R is a division algebra over k.
: 這要怎麼證呢
: 好像沒有很難卻一直想不到
: 還有前後半部的關係也看不出來
: 求教高手
: 感謝
Consider the space span by <1,s,s^2,..,>, which must be of finite diemnsion/k,
and use rs=1, one can see that
s=a_(n-1)r^(n-1)+...a_1r+a_0 for some a_i in k
then it's obvious that sr=ra=1.
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◆ From: 76.89.226.110
※ 編輯: Sfly 來自: 76.89.226.110 (09/27 15:37)