五次循环域的生成元

汤健儿

doi:10.14188/j.1671-8836.2020.0237

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五次循环域的生成元

数学 | 更新时间：2023-08-02

- 五次循环域的生成元
- Generators of Quintic Cyclic Field
- 武汉大学学报（理学版）
- 作者机构：
  
  1.上海财经大学数学学院，上海 200433
  2.上海财经大学浙江学院，浙江金华321013
- 作者简介：
  
  汤健儿，男，副教授，现从事代数与数论研究。E-mail：1277708824@qq.com
  E-mail：qxhe@mail.shufe.edu.cn
- 基金信息：
  
  国家自然科学基金(11671097);上海财经大学浙江学院发展基金(2018GR002)
- DOI：10.14188/j.1671-8836.2020.0237
  中图分类号： O156.2
- 纸质出版日期：2021-04-24，
  
  收稿日期：2020-09-29，
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引用本文
汤健儿,何其祥.五次循环域的生成元[J].武汉大学学报（理学版）,2021,67(2):143-150.

TANG Jianer,HE Qixiang.Generators of Quintic Cyclic Field [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):143-150.
汤健儿,何其祥.五次循环域的生成元[J].武汉大学学报（理学版）,2021,67(2):143-150. DOI：10.14188/j.1671-8836.2020.0237

TANG Jianer,HE Qixiang.Generators of Quintic Cyclic Field [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):143-150. DOI：10.14188/j.1671-8836.2020.0237(Ch).

摘要

五次循环域, $K$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290849&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290847&type=,3.89466667,2.37066674,作为分圆域, $Q (e^{\frac{2 π i}{m}})$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290852&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290850&type=,9.48266697,5.33399963,的子域，当, $m$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290855&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290854&type=,2.45533323,2.37066674,是单因子，即为, $p \equiv 1$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290732&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290857&type=,7.28133297,3.13266659,（mod 5）类型素数或等于25 时，构建了, $K$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290884&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290858&type=,3.21733332,2.37066674,的定义方程，并利用多个单因子域之生成元相合成的方法，对其他情形即, $m$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290861&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290885&type=,2.45533323,2.37066674,是多因子时，给出了, $K$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290864&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290886&type=,3.21733332,2.37066674,的生成元。

Abstract

Quintic cyclic field, $K$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290866&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290888&type=,3.72533321,2.37066674, is regarded as a subfield of cyclotomic field , $Q (e^{\frac{2 π i}{m}})$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290892&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290890&type=,9.48266697,5.33399963,. The defining equation of ,K, is constructed if , $m$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290899&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290867&type=,2.45533323,2.37066674, is a simple factor (it means , $p \equiv 1$ ,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290902&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46290900&type=,7.28133297,3.13266659,(mod 5) type prime number or 25). The generators of ,K, are given by combining the generators of multiple single factors when ,m, is a multiple factor.

关键词

循环和单因子循环域多因子循环域共生矩阵

Keywords

cyclic sumcyclic field of simple factorcyclic field of multiple factorconjugate matrix

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