Bourbaki

Proposition 4

Tag 06OP, permanent. Cite it as [Bourbaki, Tag 06OP].

Algebra, chapter V, § 11. Abelian extensions

— Let n≥1n \geq 1 be an integer; suppose that there exist n n-th roots of unity in K (this is true for example if K is separably closed and n.1,≠0n . 1, \neq 0). Then the number of primitive n-th roots of unity in K is equal to φ(n)\varphi(n).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

Nothing.

Transcribed from the printed edition, 2003, Springer. Not translated.