Fonctions R\'egulues
  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. 
Goulwen Fichou (IRMAR), Johannes Huisman (LM), Fr\'ed\'eric Mangolte   (LAREMA), Jean-Philippe Monnier (LAREMA)
math.AG