CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

  Published:2013-10-14
 Printed: Sep 2014
  • Adam Parusiński,
    Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
  • Jean-Philippe Rolin,
    Univ. de Bourgogne (Dijon), I.M.B., 9 av. A. Savary, BP47870, 21078 Dijon Cedex, France
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation Theorem holds in such a ring then all elements of it are germs of analytic functions.
MSC Classifications: 26E10, 26E05, 14P15 show english descriptions $C^\infty$-functions, quasi-analytic functions [See also 58C25]
Real-analytic functions [See also 32B05, 32C05]
Real analytic and semianalytic sets [See also 32B20, 32C05]
26E10 - $C^\infty$-functions, quasi-analytic functions [See also 58C25]
26E05 - Real-analytic functions [See also 32B05, 32C05]
14P15 - Real analytic and semianalytic sets [See also 32B20, 32C05]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/