If F is a field and / is the ideal (x 2 , xy) in F[x, yJ,

Question:

If F is a field and / is the ideal (x², xy) in F[x, yJ, then there are at least three distinct reduced primary decompositions of I; three such are

(i) I = (x) ∩ (x², y);

(ii) I= (x) ∩ (x², x + y);

(iii) I = (x) ∩ (x², xy, y²).

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It looks like youve provided three different reduced primary decompositions for the ideal I x2 xy in the polynomial ring Fx y Lets go through each of ...View the full answer

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