Ideals and differential operators in the ring of polynomials of infinitely many variables

Autor: Miklós Laczkovich
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