9 citations · 9 across the 2 of their papers we have counts for
5 papers · 1 filter
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.
Commutative algebra: Constructive methods. Finite projective modules
Henri Lombardi, Claude Quitté
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with…
The syzygy theorem for Bézout rings
Maroua Gamanda, Henri Lombardi, Stefan Neuwirth +1
We provide constructive versions of Hilbert's syzygy theorem for Z and Z/nZ following Schreyer's method. Moreover, we extend these results to arbitrary coherent strict Bézout ring…