The Regular Element Property in Constructive Mathematics
Thierry Coquand · arXiv (Cornell University) · 2024
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.