Editing Kronecker–Weber theorem (section)

==Generalizations==
{{harvs|txt|last1=Lubin|last2=Tate|year1=1965|year2=1966}} proved the local Kronecker–Weber theorem which states that any abelian extension of a [[local field]] can be constructed using cyclotomic extensions and [[Lubin–Tate extension]]s.   {{harvs|txt|last=Hazewinkel|year=1975}}, {{harvs|txt|last=Rosen|year=1981}} and {{harvs|txt|last=Lubin|year=1981}} gave other proofs.

[[Hilbert's twelfth problem]] asks for generalizations of the Kronecker–Weber theorem to base fields other than the rational numbers, and asks for the analogues of the roots of unity for those fields. A different approach to abelian extensions is given by [[class field theory]].