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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Fall 2021 • Question 1

Question

Math 6320 • Algebra II Fall 2021 • Question 1

Find a degree 5 monic polynomial with integer coefficients that is irreducible in \(\mathbb {Q}[x]\) but does not satisfy the Eisenstein criterion for any prime \(p\).

Raw LaTeX

Find a degree 5 monic polynomial with integer coefficients that is
irreducible in \(\mathbb{Q}[x]\) but does not satisfy the Eisenstein criterion
for any prime \(p\).

Topic Tags

Galois Groups of Polynomials Irreducible Polynomials Polynomial Rings and Prime Ideals