cyclotomic field

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cyclotomic field

[‚sī·klə¦täm·ik ′fēld]
(mathematics)
The extension field of a given field K which is the smallest extension field of K that includes the n th roots of unity for some integer n.
References in periodicals archive ?
Washington, Introduction to cyclotomic fields, 2nd ed.
n]] is the ring of integers of the nth cyclotomic field Q([[zeta].
In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields.
Certain mathematical systems, known technically as cyclotomic fields, can be constructed as generalizations of the set of rational numbers.
p]-covers Jun Ueki On the ring of integers of real cyclotomic fields Koji YAMAGATA and Masakazu YAMAGISHI Above two, communicated by Shigefumi MORI, M.
Robertson, Heuristics for class numbers of prime-power real cyclotomic fields, in High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Inst.
Let K be a cyclic field, not contained in the cyclotomic field Q([e.
Miller that his methods for finding principal ideals of real cyclotomic fields in [24], [25] may be valid for Q([[zeta].
Montgomery, Cyclotomic fields with unique factorization, J.
Washington, Quintic poly- [12] nomials and real cyclotomic fields with large class numbers, Math.
Birch, Cyclotomic fields and Kummer extensions, in Algebraic Number Theory (Proc.
p] for the cyclotomic field which is generated by the values of any (and therefore every) element of [D.