基于同态欧氏环Zp[x]的整系数多项式可约性的判定
he Determination Method About the Reduciblity of Integral Coefficient Polynomial Based on the Homomorphic Euclidean Ring
整系数多项式可约性的判定因其次数和系数的复杂性显得十分困难。欧氏环是唯一分解环,借助同态映射,利用多项式环与有限域上的欧氏环Zp[x] 同态的原理，给出判定整系数多项式可约性的一个新方法，得到关于整系数多项式在有理数域上不可约以及可约的多项式能够进行因式分解的若干条件和方法，给因式分解提供了一种新的借鉴。较传统的一些判断方法，同态原理更方便更快捷。
It is extremely difficult to determine the reduciblity of integral coefficient polynomial because of the complexity of their degree and coefficients.Euclidean ring is a unique factorization ring,and polynomial rings is homomorphism with Euclidean rings over finite field,we give a new method to determine the reducibility of integral coefficient polynomial by homomorphic principle.we can get a number of conditions about the irreduciblity and its factorization of the integral coefficient polynomial.It provides a new reference to the factorization.Comparing with traditional discriminating methods, it is more convenient and fast.
罗永超、邓从政
数学
欧氏环同态原理整系数多项式可约性有限域
Euclidean ringhomomorphic principleIntegral coefficient polynomialreduciblitythe Finite field.
罗永超,邓从政.基于同态欧氏环Zp[x]的整系数多项式可约性的判定[EB/OL].(2012-11-23)[2025-05-28].http://www.paper.edu.cn/releasepaper/content/201211-450.点此复制
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