2023/01/16 by Alonso M. -E., Alonso, M. -E., H. Lombardi +3
Mathematics · #03F65 #13B40 #13J15 #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical and Theoretical Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2301.06546
openalex publication_date 2023/01/16 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28
The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields.