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摘要翻译：
多项式系统或多项式理想的根泛函的概念是根概念的推广，特别是对于重根。根泛函是定义在多项式环上的一种线性泛函，它以多项式的理想为环。有界根泛函是这样一个泛函，它在该理想中的某些过滤中，将该理想的第d个分量环空。本文研究了方程组个数等于未知个数的多项式方程组的有界根泛函及其扩张运算。可拓运算与多元贝走田结构有联系。
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英文标题：
《Extension of bounded root functionals of a system of polynomial
equations》
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作者：
Timur R. Seifullin
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The notion of a root functional of a system of polynomials or ideal of polynomials is a generalization of the notion of a root, in particular, for a multiple root. A root functional is a linear functional that is defined on a polynomial ring and annuls the ideal of polynomials. A bounded root functional is a functional that annuls d-th component of the ideal in some filtration in this ideal. The paper consider bounded root functionals and their extension operation for a system of polynomial equation at which the number of equations is equal to the number of unknows. The extension operation has connection with the multivariate Bezoutian construction.
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PDF链接：
https://arxiv.org/pdf/0804.2420
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