8 citations · 19 across the 10 of their papers we have counts for
11 papers
Théories géométriques pour l'algèbre des nombres réels sans test de signe ni axiome de choix dépendant
Henri Lombardi, Assia Mahboubi
In this memoir, we seek to construct a dynamical theory as complete as possible to describe the algebraic properties of the field of real numbers in constructive mathematics withou…
Dimension de Krull, Nullstellensätze et Évaluation Dynamique
Henri Lombardi
We prove constructively a Nullstellensatz giving an equivalence between the existence of a certain kind of algebraic identity on one hand, and the impossibility of finding an incre…
An algorithm for computing syzygies on when is a valuation domain
Henri Lombardi, Claude Quitté, Ihsen Yengui
We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "ec…
Construction du hensélisé d'un corps valué
Henri Lombardi, Franz-Viktor Kuhlmann
We give an explicit construction of the henselization of a valued field, with a constructive proof. It is analogous to the construction of the real closure of a discrete ordered fi…
À propos d'un théorème de de Felipe et Teissier sur la comparaison de deux hensélisés dans le cas non noethérien
Maria-Emilia Alonso, Henri Lombardi, Stefan Neuwirth
This paper gives an elementary proof of a theorem by de Felipe and Teissier in the paper "Valuations and henselization" (arXiv:1903.10793v1), to appear in Math. Annalen. The theore…
Modules projectifs de type fini, applications linéaires croisées et inverses généralisés
Gema M. Díaz--Toca, Laureano Gonzalez-Vega, Henri Lombardi +1
We give a general theory of generalised inverses and we explain the link with the theory of finitely generated projective modules. All the paper is written in constrctive mathemati…
Dimension de Heitmann des treillis distributifs et des anneaux commutatifs
Thierry Coquand, Henri Lombardi, Claude Quitté
We study a notion of dimension which was introduced by R. Heitmann in his remarkable paper in 1984, and also a related notion, implicit in the proofs in his paper. We develop these…
Méthodes Matricielles Introduction à la Complexité Algébrique
Jounaïdi Abdeljaoued, Henri Lombardi
The main purpose of this book is to propose an introduction to the modern tools of algebraic complexity. To remain as simple as possible while providing meaningful examples, we cho…
Calcul matriciel généralisé sur les domaines de Prüfer
Gema M. Diaz-Toca, Henri Lombardi
In this paper, we first present an algorithm for computing the Hermite normal form of pseudo-matrices over Prüfer domains. This algorithm allows us to provide constructive proofs o…
Théorème de de Smit et Lenstra, démonstration élémentaire
Henri Lombardi, Claude Quitté
We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"
Anneaux à diviseurs et anneaux de Krull (une approche constructive)
Thierry Coquand, Henri Lombardi
We give give an elementary and constructive version of the theory of "Prüfer v-Multiplication Domains" (which we call "anneaux à diviseurs" in the paper) and Krull Domains. The mai…