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基于同态欧氏环ZP[x]的整系数多项式可约性判定

发表时间:2013-07-15  浏览量:1204  下载量:284
全部作者: 邓从政,罗永超
作者单位: 凯里学院数学科学学院
摘 要: 整系数多项式可约性的判定因其次数和系数的复杂性而十分困难。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。
关 键 词: 代数学;同态原理;可约性;整系数多项式;欧氏环
Title: Determination on reducibility of integral coefficient polynomial based on homomorphic Euclidean ring ZP[x]
Author: DENG Congzheng, LUO Yongchao
Organization: School of Mathematical Sciences, Kaili University
Abstract: It is extremely difficult to determine the reducibility of integral coefficient polynomial because of the complexity of their degree and coefficients. Euclidean ring is a unique factorization ring. Based on homomorphic mapping and homomorphism of polynomial rings with Euclidean rings ZP[x] over finite field, we gave a new method for determining the reducibility of integral coefficient polynomial. In addition, we obtained a number of conditions and methods for the reducibility irreducibility and their factorization of the integral coefficient polynomial, which provided a new reference for the factorization. In comparison with traditional discriminating methods, this method was more convenient and faster.
Key words: algebra; homomorphic principle; reducibility; integral coefficient polynomial; Euclidean ring
发表期数: 2013年7月第13期
引用格式: 邓从政,罗永超. 基于同态欧氏环ZP[x]的整系数多项式可约性判定[J]. 中国科技论文在线精品论文,2013,6(13):1182-1186.
 
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