Prime ideal decomposition in F(μ^1∕p)

William Yslas Vélez

Vol. 75 (1978), No. 2, 589–600

DOI: 10.2140/pjm.1978.75.589

Abstract

Let F be a finite extension of the field of rational numbers, 𝒫 a prime ideal in the ring of algebraic integers in F, and x^m − μ irreducible over F. If m is a prime and ζ_m ∈ F, then the ideal decomposition of 𝒫 in F(μ^1∕m) has been described by Hensel. If m = l^t, l a prime and (l,𝒫) = 1, then the decomposition of 𝒫 in F(μ^1∕lt ) was obtained by Mann and Vélez, with no restriction on roots of unity. In this paper we describe the decomposition of 𝒫 in the fields F(ζ_p) and F(μ^1∕p), where 𝒫⊃ (p).

Mathematical Subject Classification

Primary: 12A40, 12A40

Milestones

Received: 22 November 1976

Revised: 16 May 1977

Published: 1 April 1978