Seminormal Rings (following Thierry Coquand)
arXiv:2310.09763 · doi:10.1016/j.tcs.2007.10.007
Abstract
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 needed to understand the elementary constructive proof for this result given by Thierry Coquand in the paper: On seminormality. J. Algebra 305, no. 1-3, 577-584, (2006). In this new version we have fixed a little typo in Theorem 3.8: the hypothesis seminormal was missing.