Uploaded January 2021 | Updated September 2026, 2 weeks ago
This lecture is part of an online graduate course on Galois theory.
We describe Galois extensions with cyclic Galois group of order n in the case when the base field contains all n'th roots of unity and has characteristic not dividing n. We show that all such extensions are radical. As an example we express cos 2pi/7 explicitly using cube roots. Finally we mention the Kummer pairing.
This lecture is part of an online graduate course on Galois theory.
We describe Galois extensions with cyclic Galois group of order n in the case when the base field contains all n'th roots of unity and has characteristic not dividing n. We show that all such extensions are radical. As an example we express cos 2pi/7 explicitly using cube roots. Finally we mention the Kummer pairing.
