32 citations · 100 across the 24 of their papers we have counts for
6 papers · 1 filter
Hidden constructions in abstract algebra. Krull Dimension of distributive lattices and commutative rings
Thierry Coquand, Henri Lombardi
We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Españ…
Hidden constructions in abstract algebra, Krull Dimension, Going Up, Going Down
Thierry Coquand, Henri Lombardi
We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Espan…
Virtual Roots of Real Polynomials
Laureano Gonzalez--Vega, Henri Lombardi, Louis Mahé
The fact that a real univariate polynomial misses some real roots is usually overcame by considering complex roots, but the price to pay for, is a complete lost of the sign structu…
Roger Apéry: humour at the service of a free and original thinking on constructive mathematics
Henri Lombardi, Stefan Neuwirth
This article is an invitation to read a famous text of Roger Ap{é}ry, "Math{é}matique constructive", published in the book "Penser les math{é}matiques: s{é}minaire de philosophie e…
Dynamical method in algebra: Effective Nullstellensätze
Michel Coste, Henri Lombardi, Marie-Françoise Roy
We give a general method for producing various effective Null and Positivstellensätze, and getting new Positivstellensätze in algebraically closed valued fields and ordered groups.…
Lattice-ordered groups generated by an ordered group and regular systems of ideals
Thierry Coquand, Henri Lombardi, Stefan Neuwirth
Unbounded entailment relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental rôle in logic (see Scott 1974) and in algebra (see Lo…