Eisenstein判别法的变换与推广  

Transform and Extension of Eisenstein Discriminant Method

作　　者：王子茹[1] 梅瑞[1] 梁菊先[1] 

机构地区：[1]河北北方学院理学院,河北张家口075000

出　　处：《河北北方学院学报（自然科学版）》2017年第5期9-13,19,共6页Journal of Hebei North University:Natural Science Edition

基　　金：张家口市科学技术研究与发展计划项目(13110039I-4);河北北方学院教育教学改革项目(JG201545);河北北方学院自然科学研究计划项目(Q2013002)

摘　　要：目的 Eisenstein判别法并不是对所有在有理数域上的不可约整系数多项式都适用,对其实行变化与推广,从而扩大Eisenstein判别法的适用范围。方法对于整系数多项式,可以通过线性变换x=ay+b间接应用Eisenstein判别法的可能性,给出与Eisenstein判别法相对称的一种判别法。结果论述Eisenstein判别法的若干具有实用价值的推广形式,并把Eisenstein判别法推广到整环上。结论在整环上,可用Eisenstein判别法解决是否可约问题。ObjectiveEisenstein discriminant method does not apply to all the irreducible integral coefficient polynomials in rational number field.To expand the scope of the Eisenstein discriminant method,it is necessary to implement its changes and promotions.MethodsFor the integral coefficients polynomial,a discriminant method symmetric with the Eisenstein discriminant method is given within the bounds of possibility of applying integral coefficient polynomial by linear transforming x=ay+b indirectly.ResultsThe practical extensive forms of Eisenstein discriminant method are discussed and extended to integral domain.ConclusionIn integral domain,reducible problem can be solved by Eisenstein discriminant method.

关 键 词：有理数域 不可约多项式 整环 商域 唯一分解环 素理想 本原多项式 

分 类 号：O151[理学—数学]