Cyclotomic integer ($\mathbb{Z}[{\zeta }_n]$)

A cyclotomic integer is an element of $\mathbb{Z}[{\zeta }_n]$, where ${\zeta }_n$ is a root of unity. For a primitive $n$-th root, this is the full ring of integers of the cyclotomic field $\mathbb{Q}({\zeta }_n)$.