There result formulae stating that the class number is determined by the index of the cyclotomic units in the whole group of units.
32.
When n is a power of 2, the polynomial ? ( x ) will be the cyclotomic polynomial x n + 1.
33.
An important class of polynomials whose irreducibility can be established using Eisenstein's criterion is that of the cyclotomic polynomials for prime numbers.
34.
In other words, the 105th cyclotomic polynomial, & Phi; 105, is the first with coefficients other than \ pm 1.
35.
The Kronecker Weber theorem shows that any finite abelian extension of "'Q "'is contained in a cyclotomic field.
36.
This is a special case of the Chebotarev density theorem for the " N " th cyclotomic field " K ".
37.
*PM : examples of cyclotomic polynomials, id = 9688 new !-- WP guess : examples of cyclotomic polynomials-- Status:
38.
*PM : examples of cyclotomic polynomials, id = 9688 new !-- WP guess : examples of cyclotomic polynomials-- Status:
39.
Kummer set himself the task of determining whether the cyclotomic field could be generalized to include new prime numbers such that unique factorisation was restored.
40.
This failure of unique factorization in some cyclotomic fields led Ernst Kummer to the concept of ideal numbers and, later, Richard Dedekind to ideals.
