Eisenstein判别法的一个新的推广  

A New Generalization of the Eisenstein Irreducibility Criterion

作　　者：王冰 朱林 

机构地区：[1]上海立信会计金融学院统计与数学学院,上海 [2]上海理工大学理学院,上海

出　　处：《理论数学》2023年第9期2516-2519,共4页Pure Mathematics

摘　　要：本文给出了Eisenstein判别法的一个新的推广,得到了整系数多项式的不可约因式的次数估计。作为应用,若偶数次整系数多项式的系数满足某些整除关系,则该多项式在有理数域上不可约当且仅当它没有有理根。In this paper, a new generalization of the Eisenstein irreducibility criterion is given and an estimate of the degree of an irreducible factor of a polynomial with integer coefficients is obtained. As an application, if the coefficients of a polynomial with integer coefficients of even degree satisfy some divisibility conditions, then the polynomial is irreducible over the rational number field if and only if the polynomial does not have rational roots.

关 键 词：整系数多项式 不可约多项式 有理根 不可约判别法 

分 类 号：O17[理学—数学]