# nLab cyclotomic field

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

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

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

## References

Last revised on October 7, 2018 at 13:51:42. See the history of this page for a list of all contributions to it.