Eisenstein判别法及(E,p)型数域的推广  

The Generalization of Eisenstein Criterion and Number Fields of( E,p)-Type

作　　者：陶新恩 宋欣欣[1] 庄媛媛[1] 罗明[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2014年第5期85-88,共4页Journal of Chongqing Normal University:Natural Science

摘　　要：Eisenstein判别法是高等代数中判定整系数多项式在有理数域中的可约性的重要方法,其推广形式很多,而最原始的形式应用代数数论中来定义(E,p)型数域。本文在原来Eisenstein判别法的基础上进行适当地推广,并将已知的(E,p)型数域也随其判别法的推广而推广,成为广(E,p)型数域,在此基础上研究此数域的性质:给出素数p在广(E,p)型数域中的素理想分解形式,并且给出了这个素数p的一个重要性质。其次,得到广(E,p)型数域中素数p及相关理想的一些性质,并给出相应的证明。这样,就推广了原本只讨论最原始定义的Eisenstein判别法及(E,p)型数域的相关性质,使此理论更加完善。Eisenstein criterion is an important way of finding the reducibility of integer polynomial under rational number field in high- er algebra, and also a hot issue in studying polynomial. It has a great many forms of generalization, and the definition of the number fields of （E,p）-Type comes from the primitive from. On the basic of Eisenstein criterion, this paper extends the number fields of （E,i0）-Type, and then study its properties： give the decomposition of prime ideal type in the generalized number fields. The specific method： prove Lemma 3 and use point 3, then get the decomposed form of the prime ideal. And this paper give this prime an important property （refer to Theorem 1）. This is the main contents of this paper. Besides, by Theorem 1 and its proof can we get prime under generalized number fields of （E,p）-Type and some properties related to prime ideal. So we can generalize Eisenstein criterion and the number fields of （E,p）-Type and get more properties and make this theory more consummate.

关 键 词：EISENSTEIN判别法 (E  ρ)型数域 素理想 

分 类 号：O156.4[理学—数学]