多项式方程的有界根泛函的扩张
Extension of bounded root functionals of a system of polynomial equations
摘要：
多项式系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取消多项式理想的线性泛函。一个有界根泛函是一个在理想的某些滤子中取消理想的第d个分量的泛函。本文考虑方程个数等于未知数个数的多项式方程的有界根泛函及其扩张运算。扩张运算与多元Bezoutian构造有关。
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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