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

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalTokyo Journal of Mathematics
Volume11
Issue number1
DOIs
StatePublished - 1988

Fingerprint

Factorization
Genus
Restriction
Ring
Decompose
Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Factorization of p in Q(a 1/p k) and the Genus Field of Q(a1/n). / Velez, William Yslas.

In: Tokyo Journal of Mathematics, Vol. 11, No. 1, 1988, p. 1-19.

Research output: Contribution to journalArticle

@article{82b45a47468248fea747f49ce2cd6fac,
title = "The Factorization of p in Q(a 1/p k) and the Genus Field of Q(a1/n)",
abstract = "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.",
author = "Velez, {William Yslas}",
year = "1988",
doi = "10.3836/tjm/1270134258",
language = "English (US)",
volume = "11",
pages = "1--19",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "1",

}

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 -