ABSTRACT
This famous theorem asserts that every Abelian extension K of ℚ is a subfield of ℚ ( ζ m ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003177036/f0af01d0-3a24-4c34-9b44-c23e4a0fe932/content/math9_1.tif"/> for some m. These days, it is customary to obtain the Kronecker-Weber Theorem as a corollary to the main theorems of class field theory. However, we shall give an elementary proof, based essentially on that of Hilbert.
