相对二次扩张的分歧性与实二次域的基本单位

doi:10.3969/j.issn.0253-2778.2015.08.001

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (8): 623-626.DOI: 10.3969/j.issn.0253-2778.2015.08.001

• 原创论文 • 下一篇

相对二次扩张的分歧性与实二次域的基本单位

王兵

1.中国科学技术大学数学科学学院，安徽合肥 230026;2.西安电子科技大学数学与统计学院，陕西西安 710126

收稿日期:2014-11-10 修回日期:2015-07-07 出版日期:2015-08-31 发布日期:2015-08-31
作者简介:WANG Bing, male, born in 1982, PhD candidate. Research field: algebraic number theory. E-mail: wangbinx@mail.ustc.edu.cn

Ramification in relative quadratic extensions and fundamental units of real quadratic fields

WANG Bing

1.School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China; 2.School of Mathematics and Statistics, Xidian University, Xian 710126, China

Received:2014-11-10 Revised:2015-07-07 Online:2015-08-31 Published:2015-08-31
Contact: ZHANG Zhe

摘要/Abstract

摘要： 设F=Q(d)为实二次域,ε=x+yd为F的基本单位,并且ε满足NF/Q(ε)=1.建立起二次扩张F(ε)/F的二进素理想的分歧性质和x,y的同余性质之间的联系.并在d=p1…pr或2p1…pr的情形下,给出x,y的一些同余性质,其中,p1,…,pr为模4余1的不同素数.

关键词: 实二次域, 基本单位, 二进素理想, 分歧性质

Abstract: Let F=Q(d) be a real quadratic field and ε=x+yd the fundamental unit of F satisfying NF/Q(ε)=1. Some connections between the ramification properties for dyadic prime ideals in quadratic extension F(ε)/F and congruence properties of x, y were established. As a corollary, some congruence properties about x, y were given when d=p1…pr or 2p1…pr with p1≡…≡pr≡1 mod 4 being distinct prime numbers.

Key words: real quadratic field, fundamental unit, dyadic prime ideal, ramification

王兵，张哲. 相对二次扩张的分歧性与实二次域的基本单位[J]. 中国科学技术大学学报, 2015, 45(8): 623-626.

WANG Bing, ZHANG Zhe. Ramification in relative quadratic extensions and fundamental units of real quadratic fields[J]. Journal of University of Science and Technology of China, 2015, 45(8): 623-626.

相对二次扩张的分歧性与实二次域的基本单位

Ramification in relative quadratic extensions and fundamental units of real quadratic fields

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