nLab cyclotomic field

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Contents

Contents

Idea

A field extension 𝔽(ζ n)\mathbb{F}(\zeta_n) by a primitive root of unity ζ n\zeta_n.

The default meaning where 𝔽\mathbb{F} is left unspecified is 𝔽=\mathbb{F} = \mathbb{Q}, the field of rational numbers, where ζ n\zeta_n may be taken to be exp(2πi/n)\exp(2\pi i/n) (hence the smallest subfield of the complex numbers \mathbb{C} that contains this exponential value).

References

Last revised on October 25, 2023 at 12:09:54. See the history of this page for a list of all contributions to it.