Echelons of power series and Gabrielov's counterexample to nested linear Artin approximation

Herwig Hauser, Mariemi. E. Alonso, Francisco J. Castro-Jiménez

Publications: Contribution to journalArticlePeer Reviewed

Abstract

Gabrielov's famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization of the concept of ideals in power series rings.

Original languageEnglish
Pages (from-to)649-662
Number of pages14
JournalBulletin of the London Mathematical Society
Volume50
Issue number4
DOIs
Publication statusPublished - Aug 2018

Austrian Fields of Science 2012

  • 101001 Algebra
  • 101009 Geometry

Keywords

  • 13F25
  • 13P10
  • 14B12 (primary)
  • 14QXX
  • 16W60
  • 32A05

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