# Algebraic Geometry - Affine Algebraic Sets

#### Peter

##### Well-known member
MHB Site Helper
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.

Peter