Algebraic number theory MOC

Cyclotomic field

A cyclotomic field is a number field obtained by adjoining a primitive th root of unity, #m/def/num/alg i.e. , or equivalently, the splitting field of the separable polynomial

It follows that is a Finite Galois extension, with and degree given by the Euler totient function. The defining minimal polynomial of such a field is the so-called Cyclotomic polynomial.

• Its ring of integers are the Cyclotomic integers .
• See Group of roots of unity

This is especially well-behaved when is a prime power, see Prime power cyclotomic field.

Properties

1. The discriminant divides .¹

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