On Primary Decomposition of Hermite Projectors

An ideal projector on the space of polynomials C[x]=C[x1,…,xd] is a projector whose kernel is an ideal in C[x]. Every ideal projector P can be written as a sum of ideal projectors P(k) such that the intersection of their kernels kerP(k) is a primary decomposition of the ideal kerP. In this paper, we...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-09, Vol.15 (9), p.1658
Main Authors: Shekhtman, Boris, Skrzypek, Lesław, Tuesink, Brian
Format: Article
Language:English
Subjects:
Commuting
Decomposition
hermite projector
ideal projector
Kernels
Polynomials
Projectors
smoothable ideals
Variables
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Summary:An ideal projector on the space of polynomials C[x]=C[x1,…,xd] is a projector whose kernel is an ideal in C[x]. Every ideal projector P can be written as a sum of ideal projectors P(k) such that the intersection of their kernels kerP(k) is a primary decomposition of the ideal kerP. In this paper, we show that P is a limit of Lagrange projectors if and only if each P(k) is. As an application, we construct an ideal projector P whose kernel is a symmetric ideal, yet P is not a limit of Lagrange projectors.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15091658