整系数多项式不可约的一个判别法

THE CRITERION OF THE IRREDUCIBLE POLYNOMIAL OF INTEGER COEFFICIENT

本文将整系数多项式置于模p之下,然后在域p里添加其多项式的一个零点θ扩张为域p(θ)——calois域,由多项式所有零点在p(θ)域上的分布规律得出其不可约的一个判别法。

In the paper, the polynomial of integer coefficient is put under the modulo p, them in the fieldp, a null point(θ)of the polynomial of integer coefficient is added, and then its result is augmentation into the field p(θ)——Calois Field, from the distribution law of all the points of the polynomial in the field p(θ), an criterion of the irreducible polynomial of theinteger coefficient can be obtained.