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 ?
Missing coordinates are in the cyclotomic field Q[exp(2i][pi]/4)].
Let k be the cyclotomic field of p-th or 4-th roots of unity according as p > 2 or p = 2.
Washington, Introduction to cyclotomic fields, Graduate Texts in Math., vol.
It is also well known that Z[[[zeta].sub.n]] + [[[zeta].sup.-1.sub.n]]] is the ring of integers of the nth real cyclotomic field Q([[zeta].sub.n]] + [[zeta].sup.-1.sub.n]]}.
Liang, On the integral basis of the maximal real subfield of a cyclotomic field, J.
Washington, Introduction to cyclotomic fields, 2nd ed., Graduate Texts in Mathematics, 83, Springer, New York, 1997.
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.
Miller that his methods for finding principal ideals of real cyclotomic fields in [24], [25] may be valid for Q([[zeta].sub.p-1]) at least some small primes p.
Montgomery, Cyclotomic fields with unique factorization, J.
On the Iwasawa [mu]-invariants of branched [Z.sub.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.J.A.
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.