整系数多项式在有理数域上不可约判别法

Criterion for proving the irreducibility of integer polynomial in r ational field

在艾森斯坦因判别法的基础上,证明了整系数多项式在有理数域上不可约的一个判定定理,再利用模p剩余类域知识对整系数多项式的系数进行了进一步的讨论,给出了一个整系数多项式在有理数域上不可约的新的判别法。

According to the research thought of Eisenstein Criterion,the thesis offers a new method of proving the irreducibility of integer polynomial in rational field.We apply the knowledge of abstract algebra to study integral polynomials that are simplified by module p and obtain new irreducibility tests for integral polynomials.