nLab cyclotomic integer

Idea

For $\zeta_n$ an $n$th root of unity and $k$ a field, consider the cyclotomic field $k(\zeta_n)$. The ring of integers of this field is called the ring of cyclotomic integers.

Examples

• For $\mathbb{Q}$ the rational numbers, consider the cyclotomic field $\mathbb{Q}(\zeta_n)$. The ring of integers of this field is $\mathbb{Z}[\zeta_n]$, i.e. polynomials in $\zeta_n$ with integer coefficients.

• characters are cyclotomic integers

References

See also

• Wikipedia, Cyclotomic field – Properties