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| HAL: hal-00652828, version 2 |
| arXiv: 1112.3800 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-12-16) | v2 (2012-07-04) | v3 (2013-05-10) |
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| Fonctions Régulues |
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| Goulwen Fichou 1Johannes Huisman 2 |
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| (2012) |
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| 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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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Laboratoire de mathématiques de Brest (LM) |
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CNRS : UMR6205 – Université de Bretagne Occidentale [UBO] – Institut Supérieur des Sciences et Technologies de Brest (ISSTB) |
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| 3: | Laboratoire Angevin de REcherche en MAthématiques (LAREMA) |
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CNRS : UMR6093 – Université d'Angers |
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| Géométrie algébrique réelle |
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| Subject | : | Mathematics/Algebraic Geometry |
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| Attached file list to this document: | ||||||||||
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| hal-00652828, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00652828 | |
| oai:hal.archives-ouvertes.fr:hal-00652828 | |
| From: Frédéric Mangolte | |
| Submitted on: Wednesday, 4 July 2012 12:28:35 | |
| Updated on: Wednesday, 4 July 2012 13:21:25 | |
