### 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) |
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Pages (from-to) | 589-600 |

Number of pages | 12 |

Journal | Pacific Journal of Mathematics |

Volume | 75 |

Issue number | 2 |

State | Published - 1978 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Velez, W. Y. (1978). Prime ideal decomposition in F(μ

^{1/p}).*Pacific Journal of Mathematics*,*75*(2), 589-600.