A decisive Theorem (Un th\'eor\`eme d\'ecisif)
Commutative Algebra
2025-06-10 v1
Abstract
We give an elementary proof of the theorem which states that a finite unramified algebra over a discrete field is tracically \'etale. -- Nous donnons une d\'emonstration \'el\'ementaire du th\'eor\`eme selon lequel toute alg\`ebre nette sur un cors discret est \'etale, de dimension finie comme espace vectoriel et traciquement \'etale.
Cite
@article{arxiv.2506.07098,
title = {A decisive Theorem (Un th\'eor\`eme d\'ecisif)},
author = {Henri Lombardi},
journal= {arXiv preprint arXiv:2506.07098},
year = {2025}
}
Comments
in French language. Kewwords: Tracically \'etale algebra, \'Etale algebra, Unramified algebra, Unramified algebra over a discrete field, Constructive Mathematics. Mots cl\'es: Alg\`ebre traciquement \'etale. Alg\`ebre \'etale. Alg\`ebre nette. Alg\`ebre nette sur un corps discret. Math\'ematiques constructives