Prime decomposition

Abstract

Abstract In this section we describe the connection between the decomposition of prime ideals in extensions of number fields and group theory. We recall some fundamental facts from algebraic number theory and fix the notation used throughout in this book. We indicate some ideas of the proofs. Complete proofs can be found in any standard textbook on algebraic number theory (e.g. Goldstein [32], Lang [67]). For §§2-4 see also Neukirch [88], ChapterV. a. Prime ideals and residue degrees The arithmetic objects we are dealing with are the prime ideals in the ring of integers in an algebraic number field.