cyclotomic extension

《Algebra》 · 第 297 页 · Chapter V，Section 8「Cyclotomic Extensions」

A splitting field $F$ over a field $K$ of $x^n-1_K\in K[x]$ (where $n\geq 1$) is called a cyclotomic extension of order $n$.

《Introduction to Geometry (Second Edition)》 · 第 63 页 · Section 2.4「Roots of Unity and Cyclotomic Polynomials」，Definition 2.41

Let $n$ be a positive integer. The splitting field of $x^n-1$ over a field $K$ is called the $n$th cyclotomic field over $K$ and denoted by $K^{(n)}$.