Ideals and differential operators in the ring of polynomials of infinitely many variables
Autor: | Miklós Laczkovich |
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Rok vydání: | 2014 |
Předmět: | |
Zdroj: | Periodica Mathematica Hungarica. 69:109-119 |
ISSN: | 1588-2829 0031-5303 |
DOI: | 10.1007/s10998-014-0059-7 |
Popis: | Let \(\Omega \) be an uncountable and algebraically closed field. We prove that every ideal of the polynomial ring \(R=\Omega [x_1 ,x_2 ,\ldots ]\) is the intersection of ideals of the form \(\{ f\in R: D(fg)(c)=0\) for every \(g\in R\}\), where \(D\) is a differential operator of locally finite order, and \(c\) is a vector with values in \(\Omega \). |
Databáze: | OpenAIRE |
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