[代數] Module tensor product

看板Math作者 (孟新)時間15年前 (2011/02/19 05:34), 編輯推噓1(1推 0噓 7→)
留言8則, 2人參與, 最新討論串1/1
2 2 Let K be a field, B=K[x,y], and S denote the ideal (x , xy, y ) in B, regarded as a B-module. Construct a presentation for the module S ⊙ S. (That is, B n m n m free modules B and B and a homomorphism θ: B -> B such that m S ⊙ S is isomorphic to B / im(θ). ) B ⊙是tensor product因為那個符號打不出來 請問這類型的題目要怎麼做才對呢 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 128.12.114.239
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02/19 09:36, , 1F
把每個定義搞清楚, 譬如說這裡的 n 和 m 是什麼
02/19 09:36, 1F
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02/19 09:37, , 2F
然後看 tensor over B 給出了什麼 relations
02/19 09:37, 2F
推
02/19 10:54, , 3F
S⊙S = (x^4,x^3y,x^2y^2,xy^3,y^4)
02/19 10:54, 3F
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02/19 10:55, , 4F
you may choose m=5
02/19 10:55, 4F
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02/19 10:56, , 5F
and then consider 0→ker→B^5→S⊙S→0
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02/19 10:57, , 6F
然後對再做一次相同的事情..
02/19 10:57, 6F
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02/19 10:57, , 7F
你就會得到 B^n→ker→0 然後跟上面的 exact seq
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02/19 10:57, , 8F
接起來...
02/19 10:57, 8F
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