Eisenstein判别法的一个新的推广
A New Generalization of the Eisenstein Irreducibility Criterion
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。
Abstract:
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.
参考文献
|
[1]
|
张贤科, 许甫华. 高等代数学[M]. 第2版. 北京: 清华大学出版社, 2004.
|
|
[2]
|
张贤科. 抽象代数[M]. 北京: 清华大学出版社, 2022.
|
|
[3]
|
谢启鸿, 姚慕生, 吴泉水. 高等代数学[M]. 第4版. 上海: 复旦大学出版社, 2022.
|
|
[4]
|
谭玉明. 唯一分解整环上多项式不可约的一个判别法[J]. 大学数学, 2004, 20(1): 89-91.
|
|
[5]
|
罗永超. Eisenstein判别法一种新的推广及应用[J]. 数学的实践与认识, 2015, 45(19): 285-292.
|
|
[6]
|
Prasolov, V.V. (2001) Polynomi-als. In Cohen, H., Ed., Algorithms and Computation in Mathematics. Springer-Verlag, Berlin.
|