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math.AC2023★ 9 cited
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…