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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Families of Binomials
Erschienen in: Field Theory
Verlag: Springer New York
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In this chapter, we look briefly at families of binomials and their splitting fields and Galois groups. We have seen that when the base field
F
contains a primitive
n
th root of unity, cyclic extensions of degree
d
|
n
correspond to splitting fields of a single binomial
x
n
−
u
. More generally, we will see that abelian extensions correspond to splitting fields of families of binomials. We will also address the issue of when two families of binomials have the same splitting field.