Some Remarks about Normal Rings
| Affiliation auteurs | Affiliation ok |
| Titre | Some Remarks about Normal Rings |
| Type de publication | Conference Paper |
| Year of Publication | 2016 |
| Auteurs | Coquand T, Lombardi H |
| Editor | Probst D, Schuster P |
| Conference Name | CONCEPTS OF PROOF IN MATHEMATICS, PHILOSOPHY, AND COMPUTER SCIENCE |
| Publisher | WALTER DE GRUYTER GMBH |
| Conference Location | GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY |
| ISBN Number | 978-1-5015-0262-0; 978-1-5015-1080-9 |
| Mots-clés | Constructive mathematics, Gcd tree, Normal ring, Pf-ring |
| Résumé | We give a constructive proof that R[X] is normal when R is normal. We apply this result to an operation needed for studying the henselization of a local ring. Our proof is based on the casewhere R is without zero divisors, which is more involved than the case where R is an integral domain. We have to use a constructive deciphering technique that replaces the use of minimal primes (in classical mathematics) by suitable explicit localizations in a suitable tree. |