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Algebraic Geometry - Affine Algebraic Sets


Well-known member
MHB Site Helper
Jun 22, 2012
Dummit and Foote, Exercise 20, Section 15.1 reads as follows:

If f and g are irreducible polynomials in \(\displaystyle k[x,y] \) that are not associates (do not divide each other), show that \(\displaystyle \mathcal{Z} (f,g) \) is either the empty set or a finite set in \(\displaystyle \mathbb{A}^2 \).

I am somewhat overwhelmed by this problem and do not get much insight from D&F's hints on this exercise.

I would therefore appreciate someone heling me with an approach to this problem.