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

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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.

Original languageEnglish
Article number106431
JournalJournal of Pure and Applied Algebra
Volume224
Issue number12
DOIs
StatePublished - 1 Dec 2020

Keywords

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

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