cyclotomic field

Noun

cyclotomic field (plural cyclotomic fields)

1. (algebraic number theory) 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 #92;Phi#95;n(x)#61;#92;prod#95;#92;stackrel#123;1#92;lek#92;len#125;#123;#92;gcd(k,n)#61;1#125;#92;left(x-e#123;#92;frac#123;2k#92;pii#125;#123;n
   • Cyclotomic fields are fields obtained by adjoining to #92;Q roots of unity, i.e. roots of polynomials of the form Xⁿ-1, although the reader is warned that this terminology will be extended in §2.[…]Cyclotomic fields play a fundamental role in a number of arithmetic problems: for instance primes in...1991, A. Fröhlich, M. J. Taylor, “Algebraic Number Theory”, in Paperback, Cambridge University Press, published 1993, page 205