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National Repository of Grey Literature 1 records found  Search took 0.01 seconds. 
Cyclotomic extensions and the Kronecker-Weber theorem
 Jarrahová, Veronika ; Kala, Vítězslav (advisor) ; Francírek, Pavel (referee)
In the thesis, we prove the Kronecker-Weber theorem, which states that every abelian extension of the field of rational numbers is a subfield of some cyclotomic field. This theorem is traditionally proved using class field theory, but we will use an alternative relatively elementary proof using Galois theory and algebraic number theory. We will first introduce the necessary theory and show the new definitions with an example. The key part of the whole proof will be to prove the Kronecker-Weber theorem for abelian expansions of prime power degree, where only this prime ramifies. Then, we can prove relatively easily that the theorem holds for general abelian extensions. 1
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