相对二次扩张的分歧性与实二次域的基本单位（英文）  

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

作　　者：王兵[1] 张哲[2] 

机构地区：[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

出　　处：《中国科学技术大学学报》2015年第8期623-626,共4页JUSTC

基　　金：Supported by National Key Basic Research Program of China(2013CB834202);National Natural Science Foundation of China(11171317,11501429);Fundamental Research Funds for the Central Universities(JB150706)

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.Let F=QQ(d)be areal quadratic field andε=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)/Fand congruence properties of x,y were established.As a corollary,some congruence properties about x,y were given when d=p1…pror 2p1…pr with p1≡…≡pr≡1mod 4being distinct prime numbers.

关 键 词：实二次域 基本单位 二进素理想 分歧性质 

分 类 号：O156[理学—数学]