有理数域上二次单纯代数扩张同构的充要条件  

Necessary and Sufficient Condition of Isomorph for Quadratic Simple Algebraic Extensions over Rational Field

作　　者：陈功[1] 

机构地区：[1]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《南通大学学报（自然科学版）》2017年第1期87-89,共3页Journal of Nantong University(Natural Science Edition)　

基　　金：国家科技重大专项课题(2013ZX03002004)

摘　　要：通过对Q上两个二次代数元所属最小多项式系数之间关系的讨论,给出一个判定Q上二次单纯代数扩张同构的一个较为直观的充分必要条件,指出二次单纯代数扩张之间只有恒等与共轭两种同构映射.Analyzing the relationship between coefficients in minimal polynomials of two quadratic algebraic elements over rational field Q gave that a necessary and sufficient condition of isomorph for quadratic simple algebraic extensions on Q. It further showed that the isomorphism between quadratic simple algebraic extensions is either identical or conjugate.

关 键 词：有理数域 最小多项式 二次单纯代数扩张 同构 

分 类 号：O153[理学—数学]