Vol. 75, No. 2, 1978

Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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