1.Noun{\displaystyle }
A number field obtained by adjoining a primitive root of unity to the field of rational numbers.
"A cyclotomic field is the splitting field of the cyclotomic polynomial
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{\displaystyle \Phi _{n}(x)=\prod _{\stackrel {1\leq k\leq n}{\gcd(k,n)=1}}\left(x-e^{\frac {2k\pi i}{n}}\right)}
and consequently is a Galois extension of the field of rational numbers."