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

Charles Fefferman; Garving K. Luli

doi:10.4171/rmi/1218

JournalsrmiVol. 37, No. 3pp. 965–1006

Generators for the $C^{m}$ -closures of ideals

Charles Fefferman
Princeton University, USA
Garving K. Luli
University of California at Davis, USA

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Abstract

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

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