[代數] field extension and automorphism
我自己想了2個命題:
Let F be a field and K be its extension field.
Given r \in K and consider G=Aut(K/F).
(G is the group of automorphisms of K fixing F.)
Assume that [K:F] is finite. Then
1. If g(r) \in F for all nonidentity g \in G, then r \in F.
2. If g(r)=r for all g \in G, then r \in F.
---
這2個命題都可以證的出來
我的問題是:如果不是 finite extension 的話, 這2個結論會對嗎?
有沒有反例? 或是有沒有資料可以參考? 我書上都沒有找到
謝謝!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.109.105.70
推
08/22 19:29, , 1F
08/22 19:29, 1F
→
08/22 19:32, , 2F
08/22 19:32, 2F
→
08/23 08:54, , 3F
08/23 08:54, 3F
→
08/23 08:55, , 4F
08/23 08:55, 4F
推
08/23 19:06, , 5F
08/23 19:06, 5F
→
08/23 19:06, , 6F
08/23 19:06, 6F
→
08/26 13:19, , 7F
08/26 13:19, 7F
→
08/26 13:20, , 8F
08/26 13:20, 8F