### Abstract

Let x^{pk}-a be irreducible over Q. The first part of this paper is to explicitly give the decomposition rules for the factorization of p in the ring of integers of Q(a^{1/pk}). As an application of the above we use these results to determine the genus field of Q(a^{1/n}), where x^{n}-a is irreducible over Q and we make no restrictions on a.

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

Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Tokyo Journal of Mathematics |

Volume | 11 |

Issue number | 1 |

DOIs | |

State | Published - 1988 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**The Factorization of p in Q(a ^{1/p} ^{k}) and the Genus Field of Q(a^{1/n}).** / Velez, William Yslas.

Research output: Contribution to journal › Article

^{1/p}

^{k}) and the Genus Field of Q(a

^{1/n})',

*Tokyo Journal of Mathematics*, vol. 11, no. 1, pp. 1-19. https://doi.org/10.3836/tjm/1270134258

}

TY - JOUR

T1 - The Factorization of p in Q(a 1/p k) and the Genus Field of Q(a1/n)

AU - Velez, William Yslas

PY - 1988

Y1 - 1988

N2 - Let xpk-a be irreducible over Q. The first part of this paper is to explicitly give the decomposition rules for the factorization of p in the ring of integers of Q(a1/pk). As an application of the above we use these results to determine the genus field of Q(a1/n), where xn-a is irreducible over Q and we make no restrictions on a.

AB - Let xpk-a be irreducible over Q. The first part of this paper is to explicitly give the decomposition rules for the factorization of p in the ring of integers of Q(a1/pk). As an application of the above we use these results to determine the genus field of Q(a1/n), where xn-a is irreducible over Q and we make no restrictions on a.

UR - http://www.scopus.com/inward/record.url?scp=84972513729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972513729&partnerID=8YFLogxK

U2 - 10.3836/tjm/1270134258

DO - 10.3836/tjm/1270134258

M3 - Article

VL - 11

SP - 1

EP - 19

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 1

ER -