Seminormal Rings (following

The Traverso-Swan theorem says that a reduced ring A is seminormal if and only if the natural homomorphism PicA→ PicA[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 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.