| 结式与多项式互素 |
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| 引用本文： | 李冬梅,刘伟俊.结式与多项式互素[J].湖南大学学报(自然科学版),2013,40(7):95-98. |
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| 作者姓名： | 李冬梅 刘伟俊 |
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| 作者单位： | 1. 中南大学数学与统计学院,湖南长沙410075;湖南科技大学数学与计算科学学院,湖南湘潭 411201
2. 中南大学数学与统计学院,湖南长沙,410075 |
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| 基金项目： | 国家自然科学基金资助项目，湖南省教育厅资助项目 |
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| 摘 要： | 主要研究唯一分解整环上的多项式环中多元多项式互素.从一元多项式结式的经典定义出发,结合推广的结式性质,给出系数为唯一分解整环上的多个多元多项式是否互素、或是否存在非平凡公因子判定的充分必要条件.
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| 关 键 词： | 结式 多项式互素 公因子 多项式环 |
Resultants and Coprimeness of Polynomials |
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| LI Dong-mei,LIU Wei-jun.Resultants and Coprimeness of Polynomials[J].Journal of Hunan University(Naturnal Science),2013,40(7):95-98. |
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| Authors: | LI Dong-mei LIU Wei-jun |
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| Institution: | (1.School of Mathematics and Statistics, Central South Univ, Changsha, Hunan410075, China; 2.Dept of Mathematics and Computing Science, Hunan Univ of Science and Technology, Xiangtan, Hunan411201, China) |
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| Abstract: | The problem of multivariate polynomial coprime was studied, where multivariate polynomial is in polynomial rings over unique factorization domain. From the classical definition of resulatants and combining the property proposed, we obtained the necessary and sufficient condition to judge whether multivariate polynomials are coprime polynomials or not, and whether there is a common factor of positive degree in these polynomials or not. |
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| Keywords: | resultants coprime polynomials common factor polynomial ring |
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