TY - JOUR

T1 - Prime ideal decomposition in F(μ1/p)

AU - Vélez, William Yslas

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1978/4

Y1 - 1978/4

N2 - Let F be a finite extension of the field of rational numbers (Formula Precented), a prime ideal in the ring of algebraic integers in F, and xm − μ irreducible over F. If m is a prime and ζm ϵ F, then the ideal decomposition of (Formula Precented) in F(μ1/m) has been described by Hensel. If m = lt, l a prime and (l, P) = 1, then the decomposition of (Formula Precented) in F(μ1/lt) was obtained by Mann and Velez, with no restriction on roots of unity. In this paper we describe the decomposition of (Formula Precented) in the fields F(ζp) and F(μ1/p), where (Formula Precented) ⊃(p).

AB - Let F be a finite extension of the field of rational numbers (Formula Precented), a prime ideal in the ring of algebraic integers in F, and xm − μ irreducible over F. If m is a prime and ζm ϵ F, then the ideal decomposition of (Formula Precented) in F(μ1/m) has been described by Hensel. If m = lt, l a prime and (l, P) = 1, then the decomposition of (Formula Precented) in F(μ1/lt) was obtained by Mann and Velez, with no restriction on roots of unity. In this paper we describe the decomposition of (Formula Precented) in the fields F(ζp) and F(μ1/p), where (Formula Precented) ⊃(p).

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U2 - 10.2140/pjm.1978.75.589

DO - 10.2140/pjm.1978.75.589

M3 - Article

AN - SCOPUS:84972544388

VL - 75

SP - 589

EP - 600

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -