Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2017 • Question 9

Question

Math 6310 • Algebra Spring 2017 • Question 9

Let \(a\) be an integer and \(p\) a prime number such that \(x^p-a\) is reducible in \(\mathbb {Q}[x]\). Prove that \(x^p-a\) has root in \(\mathbb {Q}\).

Raw LaTeX

Let \(a\) be an integer and \(p\) a prime number such that \(x^p-a\) is reducible in \(\mathbb{Q}[x]\).
Prove that \(x^p-a\) has root in \(\mathbb{Q}\).

Topic Tags

Polynomial Rings and Ring Homomorphism Kernels