Weierstrass division theorem in definable C∞ germs in a polynomially bounded o-minimal structure
Abdelhafed Elkhadiri ; Hassan Sfouli
Annales Polonici Mathematici, Tome 89 (2006), p. 127-137 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:280422 
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     title = {Weierstrass division theorem in definable $C^{$\infty$}$ germs in a polynomially bounded o-minimal structure},
     journal = {Annales Polonici Mathematici},
     volume = {89},
     year = {2006},
     pages = {127-137},
     zbl = {1112.03033},
     language = {en},
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Abdelhafed Elkhadiri; Hassan Sfouli. Weierstrass division theorem in definable $C^{∞}$ germs in a polynomially bounded o-minimal structure. Annales Polonici Mathematici, Tome 89 (2006) pp. 127-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap89-2-2/