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

William Yslas Vélez

doi:10.3836/tjm/1270134258

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

William Yslas Vélez

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 xⁿ-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	https://doi.org/10.3836/tjm/1270134258
State	Published - Jun 1988

ASJC Scopus subject areas

General Mathematics

Access to Document

10.3836/tjm/1270134258

Cite this

@article{eaa8fd10a3e043c19c15e5c5ffa3313a,

title = "The Factorization of p in Q(a 1/pk) 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 = "V{\'e}lez, \{William Yslas\}",

year = "1988",

month = jun,

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/pk) and the Genus Field of Q(a1/n)

AU - Vélez, William Yslas

PY - 1988/6

Y1 - 1988/6

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 - https://www.scopus.com/pages/publications/84972513729

UR - https://www.scopus.com/pages/publications/84972513729#tab=citedBy

U2 - 10.3836/tjm/1270134258

DO - 10.3836/tjm/1270134258

M3 - Article

SN - 0387-3870

VL - 11

SP - 1

EP - 19

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

IS - 1

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this