Vol. 75, No. 2, 1978

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Prime ideal decomposition in F(μ1∕p)

William Yslas Vélez

Vol. 75 (1978), No. 2, 589–600

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 xm μ irreducible over F. If m is a prime and ζm F, then the ideal decomposition of 𝒫 in F(μ1∕m) has been described by Hensel. If m = lt, l a prime and (l,𝒫) = 1, then the decomposition of 𝒫 in F(μ1∕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(ζp) and F(μ1∕p), where 𝒫⊃ (p).

Mathematical Subject Classification
Primary: 12A40, 12A40
Received: 22 November 1976
Revised: 16 May 1977
Published: 1 April 1978
William Yslas Vélez