A basis for the group of units modulo ρᵐ and prime ideal decomposition in F(μ¹/ᵐ)

Abstract

In Chapter II we consider the problem of constructing an independent set of generators for the multiplicative group of units modulo ρᵐ, where ρ is a prime ideal in an algebraic number field F. Sections 4 and 5 contain a procedure for constructing such a set of independent generators. In Chapters III and IV, we consider the prime ideal decomposition of ρ in F(μ¹/ᵐ). In Chapter III we deal with the situation where (m,ρ) = 1. In Chapter IV we consider the case where m = pᶜ, p is a rational prime, and ρ ⊃ (p).