Abstract
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 nth root of unity, cyclic extensions of degree d | n correspond to splitting fields of a single binomial xn − 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.
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© 2006 Springer New York
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(2006). Families of Binomials. In: Field Theory. Graduate Texts in Mathematics, vol 158. Springer, New York, NY. https://doi.org/10.1007/0-387-27678-5_16
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DOI: https://doi.org/10.1007/0-387-27678-5_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-27677-9
Online ISBN: 978-0-387-27678-6
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