Approximation results of Artin-Tougeron-type for general filtrations and for Cr-equations

Genrich Belitskii; Alberto F. Boix; Dmitry Kerner

doi:10.1016/j.jpaa.2020.106431

Approximation results of Artin-Tougeron-type for general filtrations and for C^r-equations

Genrich Belitskii, Alberto F. Boix, Dmitry Kerner

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, {I^j}, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to C^r-rings, for 2≤r≤∞. As an auxiliary step we establish the surjectivity of the completion map [Formula presented] for a very broad class of filtrations.

Original language	American English
Article number	106431
Journal	Journal of Pure and Applied Algebra
Volume	224
Issue number	12
DOIs	https://doi.org/10.1016/j.jpaa.2020.106431
State	Published - 1 Dec 2020

Keywords

Analytic/algebraic/power series equations
Artin approximation
Germs of differentiable functions
Implicit function theorem
Tougeron approximation

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2020.106431

Cite this

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title = "Approximation results of Artin-Tougeron-type for general filtrations and for Cr-equations",

abstract = "Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, {Ij}, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to Cr-rings, for 2≤r≤∞. As an auxiliary step we establish the surjectivity of the completion map [Formula presented] for a very broad class of filtrations.",

keywords = "Analytic/algebraic/power series equations, Artin approximation, Germs of differentiable functions, Implicit function theorem, Tougeron approximation",

author = "Genrich Belitskii and Boix, {Alberto F.} and Dmitry Kerner",

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AU - Belitskii, Genrich

AU - Boix, Alberto F.

AU - Kerner, Dmitry

PY - 2020/12/1

Y1 - 2020/12/1

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AB - Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, {Ij}, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to Cr-rings, for 2≤r≤∞. As an auxiliary step we establish the surjectivity of the completion map [Formula presented] for a very broad class of filtrations.

KW - Analytic/algebraic/power series equations

KW - Artin approximation

KW - Germs of differentiable functions

KW - Implicit function theorem

KW - Tougeron approximation

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