[代數] 兩個代數問題

[bajifox (嘖)]

1. L is algebraic extension field of K,
   K is algebraic extention field of F,
   prove that L is algebraic extension field of F.

   我是想說如果a是L的元素        L
                                 |
                               K(a)
                              /    \ finite extension
                             F(a)   K
                           ?  \    /
                                 F
   ?的地方應該也可以直接得到是finite extension才是
   可是不知道怎麼做

2. Let B be a n*n matrix
   prove or disprove:
   The linear operator T on the space of all n*n matrices defined by
   T(A)=AB-BA is sigular

   試了一下應該是對的 但完全看不出為什麼會這樣= =

謝謝

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◆ From: 140.112.7.214
推 Vulpix      :2. T(I)=0, 所以有null space.
推 yusd24      :1.把係數挑出來直接做
→ bajifox     :THX