Revisiting Zariski Main Theorem from a constructive point of view
Journal article, 2014

This paper deals with the Peskine version of Zariski Main Theorem published in 1965 and discusses some applications. It is written in the style of Bishop's constructive mathematics. Being constructive, each proof in this paper can be interpreted as an algorithm for constructing explicitly the conclusion from the hypothesis. The main non-constructive argument in the proof of Peskine is the use of minimal prime ideals. Essentially we substitute this point by two dynamical arguments; one about gcd's, using subresultants, and another using our notion of strong transcendence. In particular we obtain algorithmic versions for the Multivariate Hensel Lemma and the structure theorem of quasi-finite algebras. (C) 2014 Elsevier Inc. All rights reserved.

Constructive mathematics

RINGS

Zariski Main Theorem

Quasi-finite algebras

Multivariate Hensel Lemma

Author

M. E. Alonso

Complutense University

Thierry Coquand

University of Gothenburg

H. Lombardi

University of Franche-Comté

Journal of Algebra

0021-8693 (ISSN) 1090-266X (eISSN)

Vol. 406 46-68

Subject Categories

Mathematics

DOI

10.1016/j.jalgebra.2014.02.003

More information

Created

10/10/2017