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Article Dans Une Revue Theoretical Computer Science Année : 2008

Seminormal rings (following Thierry Coquand)

Résumé

The Traverso–Swan theorem says that a reduced ring A is seminormal if and only if the natural homomorphism Pic A to Pic A[X] is an isomorphism [C. Traverso, Seminormality and the Picard group, Ann. Sc. Norm. Sup. Pisa 24 (1970) 585-595; R.G. Swan, On seminormality, J. Algebra 67 (1980) 210–229]. We give here all the details needed to understand the elementary constructive proof for this result given by Coquand in [T. Coquand, On seminormality, J. Algebra 305 (2006) 577-584]. 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 abstract 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.

Dates et versions

hal-00495326 , version 1 (25-06-2010)

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Henri Lombardi, Claude Quitté. Seminormal rings (following Thierry Coquand). Theoretical Computer Science, 2008, 3927, pp.113-127. ⟨10.1016/j.tcs.2007.10.007⟩. ⟨hal-00495326⟩
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