作者recorriendo (孟新)
看板Math
標題[代數] Module tensor product
時間Sat Feb 19 05:34:53 2011
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
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1F：→ TassTW :把每個定義搞清楚, 譬如說這裡的 n 和 m 是什麼 02/19 09:36
2F：→ TassTW :然後看 tensor over B 給出了什麼 relations 02/19 09:37
3F：推 yusd24 :S⊙S = (x^4,x^3y,x^2y^2,xy^3,y^4) 02/19 10:54
4F：→ yusd24 :you may choose m=5 02/19 10:55
5F：→ yusd24 :and then consider 0→ker→B^5→S⊙S→0 02/19 10:56
6F：→ yusd24 :然後對再做一次相同的事情.. 02/19 10:57
7F：→ yusd24 :你就會得到 B^n→ker→0 然後跟上面的 exact seq 02/19 10:57
8F：→ yusd24 :接起來... 02/19 10:57