[代數] 一題代數

看板Math作者 (adcores5)時間13年前 (2011/05/09 10:42), 編輯推噓2(2推 0噓 4→)
留言6則, 3人參與, 最新討論串6/7 (看更多)
let K be a subfield of C which is not contained in R. Prove that K is a dense subset of C -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.119.49.38
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05/09 10:55, , 1F
C/R是finite extension,所以K/R也是
05/09 10:55, 1F
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05/09 10:56, , 2F
推得K要不然是R要不然跟C同構,因此K就是C
05/09 10:56, 2F
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05/09 10:58, , 3F
抱歉 看錯了
05/09 10:58, 3F
推
05/09 11:50, , 4F
設K'= Closure of K 是體，Q<K故R<K', R=/=K'→K'=C
05/09 11:50, 4F
推
05/09 21:16, , 5F
each subfield of C contains every rational number
05/09 21:16, 5F
→
05/09 21:17, , 6F
朝這方向思考會如何勒?
05/09 21:17, 6F
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文章代碼(AID): #1DnrIRKQ (Math)
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文章代碼(AID): #1DnrIRKQ (Math)