6 papers
Azumaya algebras and Barr Theorem
Thierry Coquand, Henri Lombardi, Stefan Neuwirth
We study etale topology and the notion of Azumaya algebra over a commutative ring constructively. As an application of the syntactic version of Barr's Theorem, we show the equivale…
Seminormal Rings (following Thierry Coquand)
Henri Lombardi, Claude Quitté
The Traverso-Swan theorem says that a reduced ring A is seminormal if and only if the natural morphism from Pic(A) to Pic(A[X]) is an isomorphism. We give here all the details need…
Elementary Constructive Theory of Henselian Local Rings
Alonso GarcÃa, M. Emilia, Lombardi +3
We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.
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 group…
The Berlekamp-Massey Algorithm revisited
Nadia Ben Atti, Gema M. Diaz--Toca, Henri Lombardi
We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to expla…
Constructive theory of ordinals
Thierry Coquand, Henri Lombardi, Stefan Neuwirth
In Chapter 3 of his Notes on constructive mathematics, Martin-L{ö}f describes recursively constructed ordinals. He gives a constructively acceptable version of Kleene's computable…