The Regular Element Property in Constructive Mathematics
Commutative Algebra
2024-01-30 v1 Logic
Abstract
The goal of this note is to present Kaplansky's proof of the Regular Element Property and to explain how this argument can be adapted to the case of a coherent, strongly discrete and Noetherian (with an inductive definition of Noetherian) rings in a constructive setting. We thus get, in this setting, an algorithm which given a f.g. regular ideal, build a regular element in this ideal.
Cite
@article{arxiv.2401.15671,
title = {The Regular Element Property in Constructive Mathematics},
author = {Thierry Coquand},
journal= {arXiv preprint arXiv:2401.15671},
year = {2024}
}