Seminormal Rings (following Thierry Coquand)
Commutative Algebra
2026-03-03 v2
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.
Cite
@article{arxiv.2310.09763,
title = {Seminormal Rings (following Thierry Coquand)},
author = {Henri Lombardi and Claude Quitté},
journal= {arXiv preprint arXiv:2310.09763},
year = {2026}
}