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 ?
For any integer m [greater than or equal to] 1, the m-th cyclotomic polynomial can be defined as
Design of Efficient FIR Filters with Cyclotomic Polynomial Prefilters Using Mixed Integer Linear Programming", IEEE Signal Processing Letters, vol.
p] for the cyclotomic field which is generated by the values of any (and therefore every) element of [D.
Certain mathematical systems, known technically as cyclotomic fields, can be constructed as generalizations of the set of rational numbers.
Other topics in this first of two volumes include Wedderburn decomposition of semisimple group algebras, the group of units of an order, cyclotomic integers, K-theory, generations of unit groups of group rings, and idempotents and central units in group rings.
Iwasawa conjectured that [mu] = 0 holds for every cyclotomic [Z.
Martin and Victor Reiner, Cyclotomic and simplicial matroids, Israel J.
Topics in applications include solvability by radicals, cyclotomic extensions, geometric constructions and finite fields.
the cyclotomic character corresponding to the absolute value character v(x) = [absolute value of x] of the idele class group [A.
n]] is the ring of integers of the nth cyclotomic field Q([[zeta].
This is done using the classical cyclotomic polynomials [[PHI].