[代數] Module tensor product

[recorriendo (孟新)]

                                                     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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◆ From: 128.12.114.239
→ TassTW      :把每個定義搞清楚, 譬如說這裡的 n 和 m 是什麼
→ TassTW      :然後看 tensor over B 給出了什麼 relations
推 yusd24      :S⊙S = (x^4,x^3y,x^2y^2,xy^3,y^4)
→ yusd24      :you may choose m=5
→ yusd24      :and then consider 0→ker→B^5→S⊙S→0
→ yusd24      :然後對再做一次相同的事情..
→ yusd24      :你就會得到 B^n→ker→0  然後跟上面的 exact seq
→ yusd24      :接起來...