Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations

被引：2
|
作者：
Xiao Shuijing [1 ]
Zeng Guangxing [1 ]
机构：
[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2023年 / 36卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Polynomial ideal; rational univariate representation (RUR); valuation ring; Wu's method; SYSTEMS;
D O I：
10.1007/s11424-023-2219-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the notion of rational univariate representations with variables is introduced. Consequently, the ideals, created by given rational univariate representations with variables, are defined. One merit of these created ideals is that some of their algebraic properties can be easily decided. With the aid of the theory of valuations, some related results are established. Based on these results, a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.
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页码：2703 / 2724
页数：22
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