Generators for the Cm-closures of ideals

Charles Fefferman; Garving K. Luli

doi:10.4171/rmi/1218

Generators for the C^m-closures of ideals

Charles Fefferman, Garving K. Luli

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let R denote the ring of real polynomials on Rⁿ. Fix m ≥ 0, and let A1, . . ., AM ∈ R. The C^m-closure of (A1, . . ., AM), denoted here by [A1, . . ., AM; C^m], is the ideal of all f ∈ R expressible in the form f = F1A1 + · · · + FM AM with each Fi ∈ C^m(Rⁿ). In this paper we exhibit an algorithm for computing generators for [A1, . . ., AM; C^m].

Original language	English (US)
Pages (from-to)	965-1006
Number of pages	42
Journal	Revista Matematica Iberoamericana
Volume	37
Issue number	3
DOIs	https://doi.org/10.4171/rmi/1218
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Algorithms
Closures of ideals
Generators
Ideals
Polynomial system
Real radical
Semialgebraic differential operator
Semialgebraic sets

Access to Document

10.4171/rmi/1218

Cite this

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title = "Generators for the Cm-closures of ideals",

abstract = "Let R denote the ring of real polynomials on Rn. Fix m ≥ 0, and let A1, . . ., AM ∈ R. The Cm-closure of (A1, . . ., AM), denoted here by [A1, . . ., AM; Cm], is the ideal of all f ∈ R expressible in the form f = F1A1 + · · · + FM AM with each Fi ∈ Cm(Rn). In this paper we exhibit an algorithm for computing generators for [A1, . . ., AM; Cm].",

keywords = "Algorithms, Closures of ideals, Generators, Ideals, Polynomial system, Real radical, Semialgebraic differential operator, Semialgebraic sets",

author = "Charles Fefferman and Luli, \{Garving K.\}",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society",

year = "2021",

doi = "10.4171/rmi/1218",

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volume = "37",

pages = "965--1006",

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T1 - Generators for the Cm-closures of ideals

AU - Fefferman, Charles

AU - Luli, Garving K.

N1 - Publisher Copyright: © European Mathematical Society

PY - 2021

Y1 - 2021

N2 - Let R denote the ring of real polynomials on Rn. Fix m ≥ 0, and let A1, . . ., AM ∈ R. The Cm-closure of (A1, . . ., AM), denoted here by [A1, . . ., AM; Cm], is the ideal of all f ∈ R expressible in the form f = F1A1 + · · · + FM AM with each Fi ∈ Cm(Rn). In this paper we exhibit an algorithm for computing generators for [A1, . . ., AM; Cm].

AB - Let R denote the ring of real polynomials on Rn. Fix m ≥ 0, and let A1, . . ., AM ∈ R. The Cm-closure of (A1, . . ., AM), denoted here by [A1, . . ., AM; Cm], is the ideal of all f ∈ R expressible in the form f = F1A1 + · · · + FM AM with each Fi ∈ Cm(Rn). In this paper we exhibit an algorithm for computing generators for [A1, . . ., AM; Cm].

KW - Algorithms

KW - Closures of ideals

KW - Generators

KW - Ideals

KW - Polynomial system

KW - Real radical

KW - Semialgebraic differential operator

KW - Semialgebraic sets

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