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Journal Articles Journal für die reine und angewandte Mathematik Year : 2016

Fonctions Régulues


We study the ring of rational functions admitting a continuous extension to the real affine space. We establish several properties of this ring. In particular, we prove a strong Nullstelensatz. We study the scheme theoretic properties and prove regulous versions of Theorems A and B of Cartan. We also give a geometrical characterization of prime ideals of this ring in terms of their zero-locus and relate them to euclidean closed Zariski-constructible sets.
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Dates and versions

hal-00652828 , version 1 (16-12-2011)
hal-00652828 , version 2 (04-07-2012)
hal-00652828 , version 3 (09-05-2013)
hal-00652828 , version 4 (28-03-2014)



Goulwen Fichou, Johannes Huisman, Frédéric Mangolte, Jean-Philippe Monnier. Fonctions Régulues. Journal für die reine und angewandte Mathematik, 2016, 718 (718), pp.103-151. ⟨10.1515/crelle-2014-0034⟩. ⟨hal-00652828v4⟩
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