nLab
cyclotomic field

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 7, 2018 at 09:51:42. See the history of this page for a list of all contributions to it.