Seminormal rings (following Thierry Coquand)

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Seminormal rings (following Thierry Coquand)
The Traverso-Swan theorem says that a reduced ring A is seminormal if and only if the natural homomorphism Pic A Pic A[X] is an isomorphism ([18, 17]). We give here all the details needed to understand the elementary constructive proof for this result given by Thierry Coquand in [2]. This example is typical of a new constructive method. The final proof is simpler than the initial classical one. More important: the classical argument by absurdum using "an ideal object" is deciphered with a general technique based on the following idea: purely ideal objects constructed using TEM and Choice may be replaced by concrete objects that are "finite approximations" of these ideal objects.
Henri Lombardi, Claude Quitté
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Henri Lombardi, Claude Quitté
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