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

Abdelhafed Elkhadiri, and Hassan Sfouli. "Weierstrass division theorem in definable $C^{∞}$ germs in a polynomially bounded o-minimal structure." Annales Polonici Mathematici 89.2 (2006): 127-137. <http://eudml.org/doc/280422>.

@article{AbdelhafedElkhadiri2006,
abstract = {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 ℝⁿ, of definable $C^\{∞\}$ functions.},
author = {Abdelhafed Elkhadiri, Hassan Sfouli},
journal = {Annales Polonici Mathematici},
keywords = {o-minimal structures; power series; Weierstrass division theorem},
language = {eng},
number = {2},
pages = {127-137},
title = {Weierstrass division theorem in definable $C^\{∞\}$ germs in a polynomially bounded o-minimal structure},
url = {http://eudml.org/doc/280422},
volume = {89},
year = {2006},
}

TY - JOUR
AU - Abdelhafed Elkhadiri
AU - Hassan Sfouli
TI - Weierstrass division theorem in definable $C^{∞}$ germs in a polynomially bounded o-minimal structure
JO - Annales Polonici Mathematici
PY - 2006
VL - 89
IS - 2
SP - 127
EP - 137
AB - 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 ℝⁿ, of definable $C^{∞}$ functions.
LA - eng
KW - o-minimal structures; power series; Weierstrass division theorem
UR - http://eudml.org/doc/280422
ER -