ABSTRACT
In 1894, Hilbert developed decomposition theory to determine the factorization of a prime ideal p https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003177036/f0af01d0-3a24-4c34-9b44-c23e4a0fe932/content/math7_1.tif"/> of k in K for Galois extensions K / k https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003177036/f0af01d0-3a24-4c34-9b44-c23e4a0fe932/content/math7_2.tif"/> in terms of the Galois group Gal ( K / k ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003177036/f0af01d0-3a24-4c34-9b44-c23e4a0fe932/content/math7_3.tif"/> .
