Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 6

Question

Math 6310 • Algebra Summer 2020 • Question 6

Let \(K\) be an algebraically closed field. Let \(f\in K[x,y]\) be irreducible and let \(g\in K[x,y]\) be such that \(f\) does not divide \(g\). Prove that there is a point \((k_1,k_2)\in K^2\) such that \[ f(k_1,k_2)=0\text { and }g(k_1,k_2)\ne 0. \]

Raw LaTeX

Let \(K\) be an algebraically closed field. Let \(f\in K[x,y]\) be irreducible and let
\(g\in K[x,y]\) be such that \(f\) does not divide \(g\). Prove that there is a point
\((k_1,k_2)\in K^2\) such that
\[
f(k_1,k_2)=0\text{ and }g(k_1,k_2)\ne 0.
\]

Topic Tags

Irreducible Polynomials