7 citations · 9 across the 7 of their papers we have counts for
9 papers · 1 filter
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…
The constructive content of a local-global principle with an application to the structure of a finitely generated projective module
Henri Lombardi
We study the structure of an idempotent matrix over a commutative ring. We make explicit the fundamental system of orthogonal idempotents, hidden in this matrix, for each of wh…
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…
Some remarks about normal rings
Henri Lombardi, Thierry Coquand
We give a constructive proof that is normal when is normal. We apply this result to an operation needed for studying the henselization of a local ring. Our proof is base…
Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination
Mari-Emi Alonso, Henri Lombardi
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs a…
On a theorem by de Felipe and Teissier about the comparison of two henselisations in the non-noetherian case
María Emilia Alonso García, Henri Lombardi, Stefan Neuwirth
Let R be a local domain, v a valuation of its quotient field centred in R at its maximal ideal. We investigate the relationship between R^h, the henselisation of R as local ring, a…