Maximal ideals of regulous functions are not finitely generated
type: Item
instance of: scholarly article
title: Maximal ideals of regulous functions are not finitely generated
zbMATH Open document ID: 1402.14075
author: Aleksander Czarnecki
published in: Journal of Pure and Applied Algebra
publication date: 2018-11-09T00:00:00Z
review text: In real algebraic geometry, \(k\)-regulous functions on a real algebraic variety are introduced as a generalization of regular functions. It is known that the rings \(\mathcal{R}^k(\mathbb{R}^{N})\) of \(k\)-regulous functions on the affine space \(\mathbb{R}^{N}\) are not Noetherian for \(N\geq2\). The present paper considers maximal ideals in the rings \(\mathcal{R}^k(X)\) of \(k\)-regulous functions on a real algebraic variety \(X\) and proves the following theorem: Theorem. Assume that the real algebraic variety \(X\) is of dimension \(\geq2\) and \(k\in\mathbb{N}\). Then every maximal ideal of the ring \(\mathcal{R}^k(X)\) is not finitely generated.
reviewed by: Jie Wang
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 26C15
Mathematics Subject Classification ID: 14P20
zbMATH DE Number: 6975795
zbMATH Keywords: \(k\)-regulous function
zbMATH Keywords: maximal ideal
zbMATH Keywords: real algebraic variety
zbMATH Keywords: rational function
MaRDI profile type: Publication
full work available at URL: j.jpaa.2018.05.019
OpenAlex ID: W2807385262
cites work: Q3770650
cites work: Regulous functions
cites work: Continuous functions on the plane regular after one blowing-up
cites work: Continuous rational functions on real and \(p\)-adic varieties
cites work: Nash regulous functions
cites work: Some results of algebraic geometry over Henselian rank one valued fields
cites work: A closedness theorem and applications in geometry of rational points over Henselian valued fields
Wikidata QID: Q129741833
DOI: 10.1016/J.JPAA.2018.05.019
description: scientific article; zbMATH DE number 6975795