Note on the ring of integers of a Kummer extension of prime degree. II

被引：3

作者：

Ichimura, H ^{[1
]}

机构：

[1] Yokohama City Univ, Dept Math, Fac Sci, Kanazawa Ku, Kanagawa 2360027, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2001年 / 77卷 / 02期

关键词：

normal integral basis; tame extension; Kummer extension of prime degree;

D O I：

10.3792/pjaa.77.25

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime number, and a (is an element of Q(X)) a rational number. Then, F. Kawamoto proved that the cyclic extension Q(zeta (p) a(1/p))/Q(zeta (p)) has a normal integral basis if it is at most tamely ramified. We give some generalized version of this result replacing the base field Q with some real abelian fields of prime power conductor.

引用

页码：25 / 28

页数：4

共 50 条

[1] Note on the ring of integers of a Kummer extension of prime degree. IV
Ichimura, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2001, 77 (06) : 92 - 94
[2] Note on the ring of integers of a Kummer extension of prime degree. V
Ichimura, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2002, 78 (06) : 76 - 79
[3] Note on the ring of integers of a Kummer extension of prime degree. III
Ichimura, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2001, 77 (05) : 71 - 73
[4] A note on integral bases of unramified cyclic extensions of prime degree. II
Ichimura, H
Sumida, H
MANUSCRIPTA MATHEMATICA, 2001, 104 (02) : 201 - 210
[5] A note on integral bases of unramified cyclic extensions of prime degree. II
Humio Ichimura
Hiroki Sumida
manuscripta mathematica, 2001, 104 : 201 - 210
[6] On the ring of integers of a tame Kummer extension over a number field
Ichimura, H
JOURNAL OF PURE AND APPLIED ALGEBRA, 2004, 187 (1-3) : 169 - 182
[7] MONOGENEITY OF THE RING OF INTEGERS OF A 2P-DEGREE (P-PRIME) IMAGINARY DIHEDRAL EXTENSION
COUGNARD, J
ARCHIV DER MATHEMATIK, 1987, 48 (03) : 223 - 231
[8] Trino mixed prime number degree.
Wegner, U
MATHEMATISCHE ANNALEN, 1935, 111 : 734 - 737
[9] A note on the construction of coincidence degree.
Morassi, P
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1996, 10A (02): : 421 - 433
[10] Indices of Kummer extensions of prime degree
Maeda, Tae
Nakaya, Anri
Ota, Kaori
JOURNAL OF PURE AND APPLIED ALGEBRA, 2017, 221 (11) : 2815 - 2826

← 1 2 3 4 5 →