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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 10

Question

Math 6310 • Algebra Summer 2020 • Question 10

Let \(2^{1/4}\) be the unique positive real fourth root of of 2 in \(\mathbb {R}\). Show that \(\mathbb {Q}(2^{1/4})/\mathbb {Q}\) is not a Galois extension.

Raw LaTeX

Let \(2^{1/4}\) be the unique positive real fourth root of of 2 in \(\mathbb{R}\). Show that
\(\mathbb{Q}(2^{1/4})/\mathbb{Q}\) is not a Galois extension.

Topic Tags

Ext Functors and Module Extensions Field Extensions Galois Theory