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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:

2010年04期

Page:

28-32

Research Field:

数学

Publishing date:

Info

Title:

Power Integral Bases of Cyclotomic Field Q(ζ₄₀)

Author(s):

Shi Jun¹; Xia Jianguo²

1.School of Mathematics and Physics,Jiangsu Teachers University of Technology,Changzhou 213001,China 2. Schoo l ofM ath em at ical Scien ces, Nan jing Norm alU n iversity, Nan jing 210097, Ch ina

Keywords:

pow er integral bases;  cyclotom ic field;  generato r;  unit

PACS:

O156.2

DOI:

-

Abstract:

In this paper, we discuss the genera to rs o f powe r integra l bases of the cyc loyom ic fie ld Q(ζ_{40. W e prove that for any a lgebraic integer α∈Z(ζ40, ifα+ ?α￠ Z, then Z [α] = Z (ζ40 if and on ly ifA is equ iva lent to F40.}

References:

[ 1] Brem ne rA. On pow er bases in cyclotom ic num be r fie lds[ J] . J Number Theory, 1988, 28: 288-298.
[ 2] Robertson L. Power bases for cyclotom ic integer r ing s[ J]. J Num ber Theo ry, 1998, 69: 98-118.
[ 3] Robertson L. Power bases for 2-pow er cyclotom ic fields[ J]. J Number Theory, 2001, 88: 196-209.
[ 4] 冯克勤. 代数数论[M ]. 北京: 科学出版社, 2001. [ 5] W ash ington L J. Introduction to cyc lo tom ic Fie lds[ J]. 2nd ed. New York: Spr inge r-Ver lag, 1997.

Memo

Memo:

-

Common functions

Last Update: 2013-04-08