### Abstract

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 x^{m} − μ irreducible over F. If m is a prime and ζ_{m} ϵ F, then the ideal decomposition of (Formula Precented) 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 (Formula Precented) in F(μ^{1/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(ζ_{p}) and F(μ^{1/p}), where (Formula Precented) ⊃(p).

Original language | English (US) |
---|---|

Pages (from-to) | 589-600 |

Number of pages | 12 |

Journal | Pacific Journal of Mathematics |

Volume | 75 |

Issue number | 2 |

State | Published - 1978 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

^{1/p}).

*Pacific Journal of Mathematics*,

*75*(2), 589-600.

**Prime ideal decomposition in F(μ ^{1/p}).** / Velez, William Yslas.

Research output: Contribution to journal › Article

^{1/p})',

*Pacific Journal of Mathematics*, vol. 75, no. 2, pp. 589-600.

^{1/p}). Pacific Journal of Mathematics. 1978;75(2):589-600.

}

TY - JOUR

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

AU - Velez, William Yslas

PY - 1978

Y1 - 1978

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).

UR - http://www.scopus.com/inward/record.url?scp=84972544388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972544388&partnerID=8YFLogxK

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 -