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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2020 • Question 8

Question

Math 6310 • Algebra Spring 2020 • Question 8

Describe a primitive generator for the degree two extension of \(\mathbb {Q}\) inside the extension \(\mathbb {Q}(\zeta )\), where \(\zeta :=e^{2\pi i/7}\). Justify that the extension you identify is of degree two.

Raw LaTeX

Describe a primitive generator for the degree two extension of \(\mathbb{Q}\) inside the extension
\(\mathbb{Q}(\zeta)\), where \(\zeta:=e^{2\pi i/7}\). Justify that the extension you identify is of
degree two.

Topic Tags

Cyclotomic Fields Ext Functors and Module Extensions Field Extensions