关于整系数多项式不可约性的思考  

Reflections on Irreducibility of Integer Coefficients Polynomial

作　　者：王月明 WANG Yue-ming(Dept.of Mathematics and Physics,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院数理部,江苏南京211167

出　　处：《南京工程学院学报（自然科学版）》2018年第2期79-82,共4页Journal of Nanjing Institute of Technology(Natural Science Edition)

基　　金：江苏省自然科学基金青年基金项目(BK20160771)

摘　　要：整系数多项式的可约性与不可约性是代数学长期以来关注的主要内容.本文主要研究整系数多项式的不可约性.运用分类讨论的方法,给出在整数点有特殊取值的多项式的性质;在此基础上,利用多项式整除的性质及反证法,证明具有特殊取值的多项式不可约性,从而完善了整系数多项式不可约性的理论.The irreducibility and irreducibility of integral coefficients polynomial are essential to algebra. This paper mainly studies the irreducibility of integral coefficient polynomial. Firstly, the properties of polynomials with special values at integer points are given by using the method of classification discussion. On this basis, the irreducibility of polynomials with special values is proved by using the properties of polynomials, thereby improving the irreducibility of integral coefficients polynomial.

关 键 词：不可约多项式 整系数多项式 有理根 判别法 

分 类 号：O151[理学—数学]