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arXiv · 2401.15671

The Regular Element Property in Constructive Mathematics

Thierry Coquand
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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.

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Thierry Coquand. 2024-01-28. The Regular Element Property in Constructive Mathematics. https://arxiv.org/abs/2401.15671

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