A cyclotomic field Q(ζ) is obtained by adjoining a primitive root of unity ζ, say ζ^n = 1, to the rational numbers Q. Since ζ is primitive, ζ^k is also an nth root of unity and Q(ζ) contains all of the nth roots of unity, Q(ζ) = { sum_(k = 0)^(n - 1) a_i ζ^k :a_i element Q}.

extension field | number field