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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2016 • Question 9

Question

Math 6310 • Algebra Summer 2016 • Question 9

Show that \(K=\mathbb {Q}(\sqrt {1+\sqrt {3}})\) is not Galois over \(\mathbb {Q}\), and compute \([K:\mathbb {Q}]\).

Raw LaTeX

Show that \(K=\mathbb{Q}(\sqrt{1+\sqrt{3}})\) is not Galois over \(\mathbb{Q}\), and compute
\([K:\mathbb{Q}]\).

Topic Tags

Galois Theory Ideals in Quadratic Integer Rings and Exterior Powers