[代數] 一題關於quotient掉ideal後的dimension
Let C[x,y] be the polynomial ring with two variables over the field C
of complex numbers and let I be the ideal of C[x,y] generated by the three
polynomials
x^2+4x+4, xy+x+2y+2, y^3+3y^2+3y+1.
Compute the dimension of the quotient ring C[x,y]/I as a vector space over
C.
我把三個多項式改寫成(x+2)^2 (x+2)(y+1) (y+1)^3之後
就不知道該怎麼做了
我猜這個向量空間應該是可以用1+I (x+2)+I (y+1)+I (y+1)^2+I來當基底
所以dimension是4 請問這樣對嗎? thx
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※ 編輯: kinki5566 來自: 203.179.92.107 (01/31 21:28)
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01/31 21:29, , 1F
01/31 21:29, 1F