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
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