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20172023
most citedHidden constructions in abstract algebra. Krull Dimension of distributive lattices and commutative rings

7 citations · 9 across the 7 of their papers we have counts for

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math.AC2023

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…

math.AC2023

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…

math.AC2023

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…

math.AC20221 cited

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…

math.AC2022

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…

math.AC2020

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…