# Generators for the $C^m$-closures of ideals

### Charles Fefferman

Princeton University, USA### Garving K. Luli

University of California at Davis, USA

A subscription is required to access this article.

## Abstract

Let $\mathscr{R}$ denote the ring of real polynomials on $\mathbb{R}^{n}$. Fix $m\geq 0$, and let $A_{1},\ldots,A_{M}\in\mathscr{R}$. The $C^{m}$-closure of $(A_{1},\ldots,A_{M})$, denoted here by $[A_{1},\ldots,A_{M};C^{m}]$, is the ideal of all $f\in \mathscr{R}$ expressible in the form $f=F_{1}A_{1}+\cdots +F_{M}A_{M}$ with each $F_{i}\in C^{m}(\mathbb{R}^{n})$. In this paper we exhibit an algorithm for computing generators for $[A_{1},\ldots,A_{M};C^{m}]$.

## Cite this article

Charles Fefferman, Garving K. Luli, Generators for the $C^m$-closures of ideals. Rev. Mat. Iberoam. 37 (2021), no. 3, pp. 965–1006

DOI 10.4171/RMI/1218