Weierstrass division theorem in definable $C^{\infty}$ germs in a polynomially bounded o-minimal structure

Tom 89 / 2006

Abdelhafed Elkhadiri, Hassan Sfouli Annales Polonici Mathematici 89 (2006), 127-137 MSC: Primary 03C50, 26E10; Secondary 26E05, 03C65. DOI: 10.4064/ap89-2-2

Streszczenie

We give some examples of polynomially bounded o-minimal expansions of the ordered field of real numbers where the Weierstrass division theorem does not hold in the ring of germs, at the origin of $\mathbb{R}^n$, of definable $C^{\infty}$ functions.

Autorzy

  • Abdelhafed ElkhadiriDepartment of Mathematics
    Faculty of Sciences
    University Ibn Tofail
    BP 133 Kénitra, Morocco
    e-mail
  • Hassan SfouliDepartment of Mathematics
    Faculty of Sciences
    University Ibn Tofail
    BP 133 Kénitra, Morocco
    e-mail

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